• No results found

Structured Data

N/A
N/A
Protected

Academic year: 2021

Share "Structured Data"

Copied!
86
0
0

Loading.... (view fulltext now)

Full text

(1)

ACTA UNIVERSITATIS

UPSALIENSIS UPPSALA

2018

Digital Comprehensive Summaries of Uppsala Dissertations

from the Faculty of Science and Technology

1749

Structured Data

STEPHAN BRANDAUER

ISSN 1651-6214 ISBN 978-91-513-0515-8 urn:nbn:se:uu:diva-366932

(2)

Dissertation presented at Uppsala University to be publicly examined in Room 2446, Institutionen för informationsteknologi, Polacksbacken, Lägerhyddsvägen 2, Uppsala, Wednesday, 23 January 2019 at 13:15 for the degree of Doctor of Philosophy. The examination will be conducted in English. Faculty examiner: Professor Doug Lea (State University of New York at Oswego).

Abstract

Brandauer, S. 2018. Structured Data. Digital Comprehensive Summaries of Uppsala

Dissertations from the Faculty of Science and Technology 1749. 85 pp. Uppsala: Acta

Universitatis Upsaliensis. ISBN 978-91-513-0515-8.

References are a programming language construct that lets a programmer access a datum invariant of its location.

References permit aliasing -- several references to the same object, effectively making a single object accessible through different names (or paths). Aliasing, especially of mutable data, is both a blessing and a curse: when used correctly, it can make a programmer's life easier; when used incorrectly, for example through accidental aliases that the programmer is unaware of, aliasing can lead to hard to find bugs, and hard to verify programs.

Aliases allow us to build efficient data structures by connecting objects together, making them immediately reachable. Aliases are at the heart of many useful programming idioms. But with great power comes great responsibility: unless a programmer carefully manages aliases in a program, aliases propagate changes and make parts of a program's memory change seemingly for no reason. Additionally, such bugs are very easy to make but very hard to track down.

This thesis presents an overview of techniques for controlling how, when and if data can be aliased, as well as how and if data can be mutated. Additionally, it presents three different projects aimed at conserving the blessings, but reducing the curses. The first project is disjointness domains, a type system for expressing intended aliasing in a fine-grained manner so that aliasing will not be unexpected; the second project is Spencer, a tool to flexibly and precisely analyse the use of aliasing in programs to improve our understanding of how aliasing of mutable data is used in practise; and the third project is c flat, an approach for implementing high-level collection data structures using a richer reference construct that reduces aliasing problems but still retains many of aliasing's benefits.

Keywords: Aliasing, mutable state, imperative, programming, programming languages. Stephan Brandauer, Department of Information Technology, Division of Computing Science, Box 337, Uppsala University, SE-75105 Uppsala, Sweden.

© Stephan Brandauer 2018 ISSN 1651-6214

ISBN 978-91-513-0515-8

(3)
(4)
(5)

/LVW RI SDSHUV

7KLV WKHVLV LV EDVHG RQ WKH IROORZLQJ SDSHUV ZKLFK DUH UHIHUUHG WR LQ WKH WH[W E\ WKHLU 5RPDQ QXPHUDOV

, 'LVMRLQWQHVV 'RPDLQV IRU )LQH*UDLQHG $OLDVLQJ

6WHSKDQ %UDQGDXHU 'DYH &ODUNH 7RELDV :ULJVWDG

,QWHUQDWLRQDO &RQIHUHQFH RQ 2EMHFW2ULHQWHG 3URJUDPPLQJ 6\VWHPV /DQJXDJHV DQG $SSOLFDWLRQV 2236/$   >@

$ W\SH V\VWHP IRU H[SUHVVLQJ WKH VKDSH RI D SURJUDP¶V GDWD LQ D ILQHJUDLQHG PDQQHU

,, 6SHQFHU ,QWHUDFWLYH +HDS $QDO\VLV IRU WKH 0DVVHV

6WHSKDQ %UDQGDXHU 7RELDV :ULJVWDG

,QWHUQDWLRQDO &RQIHUHQFH RQ 0LQLQJ 6RIWZDUH 5HSRVLWRULHV 065   >@

$Q LQWHUDFWLYH WRRO IRU VLPSOH RQOLQH DQDO\VLV RI G\QDPLF H[HFXWLRQ WUDFHV RI SURJUDPV IURP VWDQGDUG SURJUDP FRUSRUD 6SHQFHU KRVWV ODUJH GDWD VHWV DQG UXQV LQ D ZHE EURZVHU PDNLQJ LW HDV\ WR JDLQ LQVLJKWV DERXW WKH EHKDYLRXU RI WKH SURJUDPV

,,, 0LQLQJ IRU 6DIHW\ XVLQJ ,QWHUDFWLYH 7UDFH $QDO\VLV

6WHSKDQ %UDQGDXHU 7RELDV :ULJVWDG

:RUNVKRS RQ 4XDQWLWDWLYH $VSHFWV RI 3URJUDPPLQJ /DQJXDJHV DQG 6\VWHPV 4$3/   >@

$Q DSSOLFDWLRQ RI 6SHQFHU 3DSHU ,, WR DQDO\VH SURJUDP WUDFHV IRU VDIHW\ SURSHUWLHV OLNH LPPXWDELOLW\ XQLTXHQHVV VWDFNERXQGHGQHVV HWF

,9 & $ 0RGXODU $SSURDFK WR (IILFLHQW DQG 7XQDEOH &ROOHFWLRQV

6WHSKDQ %UDQGDXHU (OLDV &DVWHJUHQ 7RELDV :ULJVWDG 2QZDUG  >@

$ GRPDLQ VSHFLILF ODQJXDJH DQG LWV LPSOHPHQWDWLRQ WKDW OHWV SURJUDPPHUV GHVLJQ KLJK OHYHO VWUXFWXUHV 7KHVH GDWD VWUXFWXUHV FDQ EH FRPELQHG ZLWK GLIIHUHQW ZD\V EDFNHQGV WR UHSUHVHQW GDWD LQ PHPRU\ \LHOGLQJ FROOHFWLRQV WKDW FDQ EH RSWLPLVHG E\ MXVW SLFNLQJ WKH ULJKW EDFNHQG

(6)

7KH $XWKRU¶V &RQWULEXWLRQV

, 0DLQ DXWKRU ,GHD DQG GHVLJQ E\ PDLQ DXWKRU IRUPDOLVDWLRQ DQG PDQXVFULSW ZLWK FRDXWKRUV

,, 0DLQ DXWKRU 6ROH LPSOHPHQWHU PDQXVFULSW ZLWK FRDXWKRU

,,, 0DLQ DXWKRU ([SHULPHQWV E\ PDLQ DXWKRU PDQXVFULSW LQ FROODERUDWLRQ ZLWK FRDXWKRU

,9 0DLQ DXWKRU ,GHD GHVLJQ LPSOHPHQWDWLRQ DQG HYDOXDWLRQ E\ PDLQ DX WKRU 0DQXVFULSW ZLWK FRDXWKRUV

5HODWHG 3XEOLFDWLRQV

3DUDOOHO 2EMHFWV IRU 0XOWLFRUHV $ *OLPSVH DW WKH 3DUDOOHO /DQJXDJH (QFRUH

6WHSKDQ %UDQGDXHU (OLDV &DVWHJUHQ 'DYH &ODUNH .LNR )HUQDQGH]5H\HV (LQDU %URFK -RKQVHQ

.D , 3XQ 6 /L]HWK 7DSLD 7DULID 7RELDV :ULJVWDG $OEHUW 0LQJNXQ <DQJ 

WK ,QWHUQDWLRQDO 6FKRRO RQ )RUPDO 0HWKRGV IRU WKH 'HVLJQ RI &RPSXWHU &RPPXQL FDWLRQ DQG 6RIWZDUH 6\VWHPV 0XOWLFRUH 3URJUDPPLQJ

$Q LQWURGXFWLRQ WR WKH GHVLJQ RI WKH (QFRUH SURJUDPPLQJ ODQJXDJH (QFRUH LV D SDUDO OHO REMHFWRULHQWHG SURJUDPPLQJ ODQJXDJH ZLWK DFWLYH REMHFWV WKDW FRPPXQLFDWH DV\Q FKURQRXVO\ YLD PHVVDJH SDVVLQJ DQG D W\SH V\VWHP WKDW JXDUDQWHHV GDWD UDFH IUHHGRP

7KH -RHOOH 3URJUDPPLQJ /DQJXDJH (YROYLQJ -DYD 3URJUDPV $ORQJ 7ZR $[HV RI 3DU DOOHO (YDO

-RKDQ gVWOXQG 6WHSKDQ %UDQGDXHU 7RELDV :ULJVWDG

,QWHUQDWLRQDO :RUNVKRS RQ /DQJXDJHV IRU WKH 0XOWLFRUH (UD 

$Q LQWURGXFWLRQ WR WKH -RHOOH SURJUDPPLQJ ODQJXDJH WKDW H[SORUHV WKH XVH RI RZQHUVKLS W\SHV DQG HIIHFWV DQG DFWRUV IRU EXLOGLQJ SDUDOOHO SURJUDPV VDIHO\

(7)

&RQWHQWV

3DUW , ,QWURGXFWLRQ                                                                                           

 2YHUYLHZ                                                                                                    

 %DFNJURXQG                                                                                     

 &RQWULEXWLRQV                                                                                  

 $ 6KRUW +LVWRU\ RI 5HIHUHQFHV                                                       

 5HIHUHQFHV IRU '\QDPLFDOO\ 6L]HG 'DWD 6WUXFWXUHV       

 5HIHUHQFHV )RU &RQVWDQW 7LPH 3DVVLQJ RI /DUJH 'DWD 

 5HIHUHQFHV )RU 6KDULQJ RI 0XWDEOH 6WDWH                       

 8QLQWHQGHG 6KDULQJ RI 0XWDEOH 6WDWH                            

 5HVWULFWLQJ $OLDVLQJ $ 7D[RQRP\                                                

 )RUPV RI ,PPXWDELOLW\ $ 7D[RQRP\                                          

 /DQJXDJH $EVWUDFWLRQV IRU $OLDV &RQWURO                                                 

 5HVWULFWLQJ $OLDVLQJ                                                                        

 (QFDSVXODWLRQ RI 0XWDEOH 6WDWH                                      

 $OLDV &RQWURO E\ 6XEGLYLVLRQV RI WKH +HDS                    

 8QLTXHQHVV /LQHDU 7\SHV 3HUPLVVLRQV                        

 6XPPDU\                                                                           

 3UHYHQWLQJ 0RGLILFDWLRQ                                                                 

 ,PPXWDELOLW\ WKURXJK 5HDG2QO\ 5HIHUHQFHV                

 /LPLWDWLRQV RI 5HIHUHQFH,PPXWDELOLW\                          

 ,PPXWDELOLW\ 7KURXJK )XQFWLRQDO 'DWD 6WUXFWXUHV        

 6XPPDU\                                                                                         

 0LQLQJ IRU $OLDV &RQWURO                                                                           

 0LQLQJ 7HFKQLTXHV                                                                         

 6QDSVKRW DQG 7UDFH$QDO\VLV                                         

 +RZ &RPPRQ 8QLTXHQHVV (QFDSVXODWLRQ DQG ,PPXWDELOLW\ DUH LQ 3UDFWLFH                                                                                  

 ,PPXWDELOLW\                                                                    

 8QLTXHQHVV DQG (QFDSVXODWLRQ                                        

 &RQFOXVLRQ                                                                                                  

(8)
(9)

6XPPDU\ LQ 6ZHGLVK

5HIHUHQVHU lU HQ SURJUDPVSUnNVNRQVWUXNWLRQ VRP DEVWUDKHUDU GDWRUQV PLQQH JHQRP DWW OnWD SURJUDP PDQLSXOHUD GDWD VRP lU EHOlJHW Sn DEVWUDNWD SODWVHU 'HWWD WLOOnWHU HQ SURJUDPPHUDUH DWW VNULYD NRG VRP EHKDQGODU GDWD RDYKlQJLJW GHVV SODFHULQJ L PLQQHW RFK VNDSD GDWDVWUXNWXUHU VRP NDQ Yl[D RFK NU\PSD G\QDPLVNW JHQRP DWW IOHUD GDWXP OlQNDV VDPPDQ (Q JUDI NDQ WLOO H[HPSHO UHSUHVHQWHUDV VRP HWW DQWDO REMHNW QRGHU VRP KnOOHU UHIHUHQVHU NDQWHU WLOO DQGUD REMHNW 5HIHUHQVHU WLOOnWHU YLGDUH DOLDVHULQJ ± DWW HWW REMHNW lU QnEDUW L HWW SURJUDP YLD IOHUD ROLND QDPQ 8W|YHU GHVV XSSHQEDUD Q\WWD I|U DWW UHSUH VHQWHUD VWUXNWXUHU ± VRP JUDIHU ± GlU F\NOHU HOOHU IOHUD YlJDU WLOO VDPPD SODWV I|UHNRPPHU QDWXUOLJW DQYlQGV DOLDVHULQJ W\SLVNW I|U DWW HIIHNWLYW GHOD PLQQH PHOODQ GHODU DY HWW SURJUDP HOOHU WUDYHUVHUD HQ GDWDVWUXNWXU WH[ I|OMD HQ VH ULH DY OlQNDU PHOODQ REMHNW I|U DWW V|ND HIWHU HWW HOHPHQW L HQ YLVV RUGQLQJ (Q QHJDWLY VLGRHIIHNW DY GHWWD EUXN DY UHIHUHQVHU lU DWW EnGH SURJUDPORJLN RFK SUHVWDQGD NQ\WV WLOO KXU GDWD lU UHSUHVHQWHUDW L PLQQHW ± MX IOHU OlQNDU PHOODQ REMHNW GHVWR HIIHNWLYDUH NDQ YL Qn IUDP WLOO HQ YLVVD SODWV L VWUXNWXUHQ PHQ WLOO SULVHW DY PHU NRPSOH[D UHIHUHQVVWUXNWXUHU VRP PnVWH XQGHUKnOODV RFK VRP J|U GHW VYnUDUH DWW UHVRQHUD RP SURJUDPV NRUUHNWKHW VRP YL VQDUW VNDOO VH

5HIHUHQVNRQVWUXNWLRQHQ KDU VLQ XSSULQQHOVH L VSUnNHW 3/, Sn WDOHW RFK EOHY WLGLJW NlQG VRP EnGH NUDIWIXOO RFK EHKlIWDG PHG SUREOHP 'HVVD SUREOHP XSSNRPPHU VlUVNLOW QlU UHIHUHQVHU DQYlQGV I|U DWW GHOD I|UlQGHUOLJW GDWD 2P HWW REMHNW O GHODV PHOODQ ± DOLDVHUDV DY ± IOHUD VWXNWXUHU A RFK B VlJ EOLU DOO I|UlQGULQJ YLD A RFNVn V\QOLJ IUnQ B RFK WYlUWRP 6RP HQ NRQVHNYHQV DY GHWWD PnVWH GlUI|U DOOD I|UlQGULQJDU DY O WD KlQV\Q WLOO DOOD I|UYlQWQLQJDU Sn O IUnQ EnGH A RFK B RFK DOOD DQGUD VWXNWXUHU VRP O lU HQ GHO DY  $WW KnOOD UHGD Sn YLOND VWUXNWXUHU HWW REMHNW lU GHO DY YLG YDUMH JLYHQ WLGSXQNW HOOHU PHU JHQHUHOOW YHP VRP EOLU SnYHUNDG DY HQ I|UlQGULQJ EOLU GlUI|U DY \WWHUVWD YLNW I|U HWW SURJUDPV NRUUHNWKHW 'HWWD I|UVYnUDV DY DWW VWUXNWXUHU E\JJV XSS RFK I|UlQGUDV G\QDPLVNW XQGHU N|UQLQJ ± RFK DWW GHW LQWH lU V\QOLJW L NRGHQ KXUXYLGD HQ I|UlQGULQJ DY O lU V\QOLJ I|U EDUD A I|U EDUD B HOOHU I|U EnGH A RFK B

bPQHW I|U GHQQD DYKDQGOLQJ lU UHIHUHQVHU WHNQLNHU I|U DWW XQGYLND SUREOHP PHG UHIHUHQVHU JHQRP DWW XQGYLND DOLDVHULQJ HOOHU DOLDVHULQJ DY I|UlQGHUOLJW GDWD RFK WHNQLNHU VRP WLOOnWHU DOLDVHULQJ XQGHU NRQWUROOHUDGH IRUPHU

, LQOHGQLQJHQ JHU YL HQ |YHUVLNW RFK HQ NDWHJRULVHULQJ DY H[LVWHUDQGH WHNQLNHU I|U SURJUDPPHULQJ PHG UHIHUHQVHU 9nU K\SRWHV lU DWW SURJUDPVSUnN JHU IUL KHWHU DWW DQYlQGD UHIHUHQVHU VRP GH IOHVWD SURJUDP LQWH DQYlQGHU HOOHU EHK|YHU RFK DWW GHWWD J|U GHW VYnUDUH I|U SURJUDPPHUDUH YHUNW\J RFK NRPSLODWRUHU DWW UHVRQHUD RP HWW SURJUDPV EHWHHQGH

)|U DWW XQGHUV|ND GHQQD K\SRWHV XWYHFNODU YL HWW YHUNW\J ± 6SHQFHU ± VRP VSnUDU KXU UHIHUHQVHU VNDSDV DQYlQGV RFK I|UVW|UV L SURJUDP RFK DQYlQGHU GHW Sn IOHUD YlONlQGD SURJUDP 9L ILQQHU DWW WURWV DWW DOOD UHIHUHQVHU L GH IOHVWD SUR JUDPVSUnN WLOOnWV YDUD DOLDV RFK WLOO \WWHUPHUD YLVVR I|UlQGUDV lU GHWWD RYDQOLJW 

(10)

RFK I|OMHU RIWD YLVVD P|QVWHU 6SHQFHU lU E\JJW I|U UHSURGXFHUEDU IRUVNQLQJ ± GDWD ODJUDV L PROQHW UHVXOWDW GHODV HQNHOW PHOODQ IRUNDUH RFK GHW lU HQNHOW DWW E\JJD YLGDUH Sn RFK I|UILQD QnJRQV UHVXOWDW

9L VNDSDU \WWHUOLJDUH WYn V\VWHP I|UVW ³GLVMRLQWQHVV GRPDLQV´ VRP lU HWW V\VWHP VRP OnWHU SURJUDPPHUDUH XWWU\FND YLONHQ DOLDVHULQJ VRP lU P|MOLJW L HWW SURJUDP Sn HWW SUHFLVW VlWW 'HWWD V\VWHP lU NUDIWIXOOW RFK EHYLVDW NRUUHNW PHQ VYnUW DWW XWYlUGHUD IXOOW XW HIWHUVRP GHW lU VNDSDW I|U HWW HQNHOW IRUVNQLQJVVSUnN 9L E\JJHU YLGDUH Sn UHVXOWDWHQ IUnQ 6SHQFHU RFK GLVMRLQWQHVV GRPDLQV LVWlOOHW I|U DWW I|UKLQGUD DOLDVHULQJ HOOHU NRQWUROOHUD I|UlQGULQJDU DEVWUDKHUDU YL UHIHU HQVNRQVWUXNWLRQHQ \WWHUOLJDUH L ³&´ RFK WLOOnWHU HQGDVW DWW UHIHUHQVHU DQYlQGV I|U WUDYHUVHUD HQ GDWDDVWUXNWXU L HQOLJKHW PHG HWW I|UGHILQLHUDW SURWRNROO WH[ VRP RP GDWVWUXNWXUHQ YDU HWW WUlG  'HWWD WLOOnWHU RVV DWW OnWD UHIHUHQVHU SHND Sn DEVWUDNWD REMHNW YLONHW L VLQ WXU J|U GHW P|MOLJW DWW VHSDUHUD ORJLNHQ VRP LPSOH PHQWHUDU HQ DEVWUDNW GDWDW\S IUnQ KXU GHQ lU UHSUHVHQWHUDG L PLQQHW 'HWWD J|U GHW P|MOLJW DWW MXVWHUD SUHVWDQGD XWDQ DWW lQGUD L ORJLNHQ RFK XWDQ NRPSOLFHUDGH UHIHUHQVVWUXNWXUHU

7KDQNV EXW QRW *RRGE\H

, ZDQW WR WDNH VRPH WLPH WR WKDQN WKH SHRSOH WKDW KDYH PDGH P\ WLPH GXULQJ P\ 3K' VWXGLHV LQ 8SSVDOD VR PXFK PRUH HQMR\DEOH

7RELDV \RX KDYH EHHQ D JUHDW DGYLVRU RYHU WKH ODVW ILYH \HDUV 2WKHU WKDQ DOZD\V KDYLQJ P\ EDFN \RX¶YH WDXJKW PH D ORW DERXW WHDFKLQJ ZKHUH , PDGH VRPH RI P\ PRVW PHPRUDEOH H[SHULHQFHV DV D 3K' VWXGHQW 2XU JURXS LV VR WLJKWNQLW ZH WUHDW HDFK RWKHU PRUH OLNH IULHQGV WKDQ OLNH FROOHDJXHV , WKLQN WKDW \RXU LQIOXHQFH KDV EHHQ UHVSRQVLEOH IRU D ORW RI WKLV SRVLWLYH FOLPDWH 7KDQN \RX IRU \RXU SDWLHQFH ZLWK PH

'DYH , ZLOO PLVV WKH ZHHNO\ PHHWLQJV WKH IXQ ZH KDG WKH GHVLJQ GLVFXV VLRQV DERXW (QFRUH QHHGV PRUH PRQDGV  ,¶P KDSS\ WKDW \RX MRLQHG RXU GDLO\ VWHSFRXQW FRPSHWLWLRQ EXW ,¶P QRW VR WKULOOHG DERXW WKH GLVWDQFHV \RX DUH ZDON LQJ

.LP , FDQ QRW GHVFULEH KRZ JODG , DP WR KDYH \RX 'XULQJ WKHVH ILYH \HDUV WKHUH ZHUH XSV DQG GRZQV LQ P\ ZRUN DQG \RX¶YH DOZD\V EHHQ WKHUH IRU PH , KRSH WKDW RQH GD\ , FDQ UHSD\ \RX IRU \RXU QHYHUHQGLQJ NLQGQHVV \RXU SDWLHQFH WKH VRXUGRXJK EUHDG WKH VPLOHV WKDW \RX SXW RQ P\ IDFH ZKHQ ,¶P WLUHG ,¶P QRW VXUH LI ,¶OO PDQDJH EXW , KDYH D OLIHWLPH WR WU\ P\ EHVW , ORYH \RX

)HOL[ VLQFH \RX ZHUH ERUQ HYHU\WKLQJ LV GLIIHUHQW <RX KDYH FKDQJHG P\ OLIH FRPSOHWHO\ DQG , ORYH HYHU\ ELW RI P\ QHZ OLIH , FDQ¶W ZDLW WR JR RQ SDUHQWDO OHDYH ZLWK \RX , ORYH \RX

(OLDV ZH VWDUWHG RXU 3K' DW URXJKO\ WKH VDPH WLPH DQG , DOZD\V FRQVLGHUHG WKH WZR RI XV WR EH ³LQ WKLV WRJHWKHU´ ,W ZDV JUHDW WR KDYH \RX DV D FROOHDJXH WR VKDUH DQ RIILFH ZLWK JR WR WKH EHVW VXPPHU VFKRRO HYHU ZLWK DQG WKH VHF 

(11)

RQG EHVW  DUJXH DERXW NHWFKXS LQYHQW ³FODSLWDO OHWWHUV´ ZLWK ZRUN ZLWK DW WKH ZKLWHERDUG DQG LQ WKH FODVV URRP 7KDQN \RX IRU KDYLQJ EHHQ VXFK D JUHDW FROOHDJXH DQG WKDQN \RX IRU WHDFKLQJ PH VR PXFK RYHU WKH \HDUV

.LNR $OEHUW 3KXF ,¶P UHDOO\ JODG WR KDYH KDG \RX DV FROOHDJXHV :H KDG SOHQW\ RI IXQ DQG , OHDUQHG ORWV IURP \RX JX\V , ZLOO DOZD\V UHPHPEHU KRZ PXFK IXQ ZH KDG DW WKH ODE RXWLQJV WKH FRIIHH EUHDNV ZH KDG WRJHWKHU 7KDQN \RX

$QGUH *UHJ WKH WZR RI \RX KDYH VR RIWHQ PDQDJHG WR WDNH P\ PLQG RII ZRUN , RZH \RX 7KDQN \RX IRU DOO WKH IXQ ZH KDG WRJHWKHU WKDQN \RX IRU WKH ODWH QLJKW FRQYHUVDWLRQV WKDQN \RX IRU EHLQJ VXFK JUHDW XQFOHV WR )HOL[

$QGUHDV $QNH $UYH $VWULG %HDWULFH 'DYLG *UHJ *XVWDI .MHOO 0DJQXV /nQJ 1RUJUHQ DQG 6MlODQGHU  0LKDLO 6WDYURV DQG WKRVH , KDYH IRUJRWWHQ ,¶P JODG WR KDYH EHHQ KHUH ZLWK \RX DOO /HWV VWD\ LQ FRQWDFW

0XP DQG GDG \RX KDYH DOZD\V EHOLHYHG LQ PH DQG VXSSRUWHG PH :LWKRXW \RX VR PXFK ZRXOG QRW KDYH EHHQ SRVVLEOH 7KDQN \RX IRU DOO RI WKDW

0\ ELJ EURWKHUV WKH LQIOXHQFH RI RQH RI \RX JRW PH LQWHUHVWHG LQ FRPSXWHUV WKH LQIOXHQFH RI WKH RWKHU JRW PH LQWHUHVWHG LQ DFDGHPLD %XW WKHVH DUH RQO\ WKH OLWWOH WKLQJV *URZLQJ XS ZLWK \RX KDV GHILQHG PH LQ VR PDQ\ JRRG ZD\V ± \RX¶UH DZHVRPH

(12)
(13)

3DUW ,

(14)
(15)

 2YHUYLHZ

$ UHIHUHQFH LQ SURJUDPPLQJ LV D ODQJXDJH FRQVWUXFW WKDW FDQ EH XVHG WR LQGL UHFWO\ DFFHVV D GDWXP DW DQ\ ORFDWLRQ LQ PHPRU\ 5HIHUHQFHV DUH KDQGOHV WKDW FDQ EH VWRUHG LQ YDULDEOHV RU ILHOGV DQG WKDW DOORZ DFFHVVLQJ DQ REMHFW DW D GLI IHUHQW ORFDWLRQ LQ PHPRU\ 6HYHUDO UHIHUHQFHV FDQ H[LVW WKDW UHIHU WR WKH VDPH GDWXP :KHQ VHYHUDO UHIHUHQFHV WR D GDWXP H[LVW ZH FDOO WKH UHIHUHQFHV DV ZHOO DV WKH YDULDEOHV FRQWDLQLQJ WKHP DOLDVHV DQG WKH GDWXP DOLDVHG

'HILQLWLRQ  $OLDV 7ZR UHIHUHQFHVÿDQGĀDUH DOLDVHV LI WKH\ UHIHU WR WKH VDPH REMHFW 7KH WHUP ³DOLDVLQJ´ VWHPV IURP WKH IDFW WKDW D VLQJOH REMHFW KDV VHYHUDO QDPHVÿDQGĀ ,I WZR YDULDEOHV FRQWDLQ WKHVH UHIHUHQFHV ZH DOVR FDOO WKH YDULDEOHV DOLDVHV

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

7KH VLWXDWLRQ LV ZH WKLQN UHPLQLVFHQW RI XQVWUXFWXUHG FRGH LQ WKH V SURJUDPPHUV VORZO\ PRYHG DZD\ IURP ³VSDJKHWWL FRGH´ DQG VWDUWHG XVLQJ WHFK QLTXHV RI VWUXFWXUHG SURJUDPPLQJ >@ ²LH ORRSV DQG IXQFWLRQ FDOOV 7KLV WKHVLV LV DERXW VWUXFWXUHG GDWD $W WKH KHDUW RI WKH LVVXH ZH DUH DGGUHVVLQJ OLHV D IXQGDPHQWDO GLVFRQQHFW VLPLODU WR WKH RQH SURSRQHQWV RI VWUXFWXUHG SURJUDP PLQJ IRXQG ZKLOH PRVW SURJUDPV XVH GDWD WKDW LV VWUXFWXUHG PRVW REMHFWV KDYH IHZ DOLDVHV HQFDSVXODWLRQ LV FRPPRQ HWF  SURJUDPPLQJ ODQJXDJHV SURYLGH OLWWOH PHDQV RI GRFXPHQWLQJ XQGHUVWDQGLQJ RU RSWLPLVLQJ WKDW VWUXFWXUH &RGH WKDW XVHV PXFK DOLDVLQJ ORRNV VLPLODU WR FRGH WKDW XVHV OLWWOH

 %DFNJURXQG

7KHUH LV D YDVW DPRXQW RI WHFKQLTXHV WR PLWLJDWH WKH ULVNV WKDW DOLDVLQJ RI PX WDEOH VWDWH EULQJV ZLWK LW 7KLV LQWURGXFWLRQ FKDSWHU FRYHUV D IUDFWLRQ RI WKHVH WHFKQLTXHV 7KH UDQJH RI LGHDV SUHVHQWHG KHUH LV YDU\ ZLGH ZH ZLOO FRYHU 

(16)

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

2XU PDLQ JRDO IRU WKLV FKDSWHU LV WR PDNH WKH UHDGHU XQGHUVWDQG WZR WKLQJV  +RZ ODUJH WKH QXPEHU RI WHFKQLTXHV LV WKDW UHVHDUFKHUV DQG SUDFWLWLRQ HUV KDYH FRPH XS ZLWK WR WU\ DQG VROYH WKLV SUREOHP DQG KRZ VPDOO LQ FRPSDULVRQ WKH QXPEHU RI EDVLF FRQFHSWV EHLQJ XVHG LV PRVW QRWDEO\ XQLTXHQHVV HQFDSVXODWLRQ DQG LPPXWDELOLW\ LQ YDULRXV IRUPV 

 +RZ WKH UHVHDUFK ZH KDYH FRQGXFWHG ILWV LQWR WKLV FRQWH[W E\ UHO\LQJ RQ PDQ\ RI WKH VDPH LGHDV

 &RQWULEXWLRQV

7KH FRQWULEXWLRQV RI WKLV WKHVLV DUH SUHVHQWHG LQ WKH VXEVHTXHQW FKDSWHUV 7KH ZRUN FRYHUV D ZLGH UDQJH RI UHVHDUFK WKDW LV DOO DLPLQJ WR XQGHUVWDQG DQG FRSH ZLWK DOLDVLQJ LQ LPSHUDWLYH SURJUDPPLQJ

,Q SDUWLFXODU WKH WKHVLV PDNH WKH IROORZLQJ FRQWULEXWLRQV

 D QRYHO W\SH V\VWHP IRU H[SUHVVLQJ VWUXFWXUH LQYDULDQWV RI SURJUDPV  D WRRO WR DQDO\VH G\QDPLF SURJUDP WUDFHV WKDW ZH DSSO\ WR ORRN IRU HYL

GHQFH WKDW SURJUDP PHPRU\ LV KLJKO\ VWUXFWXUHG LQ SUDFWLFH DQG

 DQ HPEHGGHG GRPDLQ VSHFLILF ODQJXDJH IRU GDWDVWUXFWXUH LPSOHPHQWD WLRQV WKDW UHPRYHV DOLDVLQJ IURP LWV VHPDQWLFV DOWRJHWKHU EXW UHFRYHUV PXFK RI WKH SHUIRUPDQFH EHQHILWV RI DOLDVLQJ E\ XVLQJ KLJKOHYHO RSWLPL VDWLRQV RI ZKROH GDWD VWUXFWXUHV

 $ 6KRUW +LVWRU\ RI 5HIHUHQFHV

%HIRUH ZH FDQ WDON DERXW KRZ UHIHUHQFHV DUH SUREOHPDWLF DQG ZKDW WR GR DERXW WKDW ZH QHHG WR XQGHUVWDQG WKH UHDVRQV IRU ZK\ UHIHUHQFHV H[LVW LQ WKH ILUVW SODFH $V UHIHUHQFHV KDYH EHHQ LQ SURJUDPPLQJ XVH IRU VR ORQJ LW LV HDV\ WR IRUJHW WKRVH UHDVRQV

+DUROG : /DZVRQ UHFHLYHG WKH ,((( &RPSXWHU 3LRQHHU $ZDUG LQ  IRU WKH LQYHQWLRQ RI SRLQWHUV DQG WKHLU LPSOHPHQWDWLRQ LQ WKH 3/, SURJUDP PLQJ ODQJXDJH LQ ± >@ 3RLQWHUV DUH YDULDEOHV WKDW VWRUH WKH PHPRU\ 

(17)

DGGUHVV RI D GDWXP 3RLQWHUV DUH D NLQG RI UHIHUHQFH EXW UHIHUHQFHV PD\ EH LPSOHPHQWHG LQ RWKHU ZD\V OLNH DV LQWHJHU LQGH[HV LQWR DQ DUUD\ 

7KH SRLQWHU FRQFHSW ZDV JURXQGEUHDNLQJ DW WKH WLPH DV LW HQDEOHG VHYHUDO LPSRUWDQW IHDWXUHV DPRQJVW WKHP

± 7KH LPSOHPHQWDWLRQ RI G\QDPLFDOO\ VL]HG GDWD VWUXFWXUHV LQ D KLJK OHYHO ODQJXDJH 6HFWLRQ  

± FRQVWDQWWLPH SDVVLQJ RI ODUJH GDWD VWUXFWXUHV 6HFWLRQ   ± VKDULQJ RI PXWDEOH GDWD IURP VHYHUDO ORFDWLRQV 6HFWLRQ  

 5HIHUHQFHV IRU '\QDPLFDOO\ 6L]HG 'DWD 6WUXFWXUHV

8VLQJ UHIHUHQFHV ZH FDQ LPSOHPHQW G\QDPLFDOO\ VL]HG GDWD VWUXFWXUHV $ SRLQWHU DOZD\V KDV WKH VDPH VL]H WKH OHQJWK RI D YLUWXDO PHPRU\ DGGUHVV LQ PHPRU\ UHJDUGOHVV RI WKH VL]H RI WKH GDWXP SRLQWHG DW 7KLV LV FUXFLDO IRU GH WHUPLQLQJ WKH VL]H RI D UHFXUVLYH GDWD W\SH D W\SH WKDW FRQWDLQV YDOXHV RI W\SH

`RU SRLQWHUV WR` $V DQ H[DPSOH FRQVLGHU D OLQNHG OLVW $ QRGH LQ D OLQNHG

OLVW FRQVLVWV RI D YDOXH KHUH FDOOHG ³HOHPHQW´  DQG D SRLQWHU WR D IROORZLQJ QRGH²LW LV D UHFXUVLYHO\ GHILQHG GDWD W\SH EHFDXVH WKH QRGH FRQWDLQV D ILHOG SRLQWLQJ WR DQRWKHU QRGH

,Q WKH & SURJUDPPLQJ ODQJXDJH D QRGH FRXOG EH GHFODUHG OLNH WKLV

âéÞî’é ϩ ¯Èé œÁœÇœÈéϝ

âéÞî’é ÈϘœ ώȜÿéϝ  QH[W SRLQWV DW WKH IROORZLQJ QRGH RU LV 18//

Ϫ ÈϘœϝ

7KH VL]H RI VXFK D OLVW LQ PHPRU\ PLJKW EH GHILQHG VLPSO\ DV WKH VXP RI WKH VL]H RI LWV FRQVWLWXHQW ILHOGV ,Q WKLV FDVH WKH VXP RI WKH VL]H RI DQ LQWHJHU IRU WKHœÁœÇœÈé ILHOG DQG D SRLQWHU IRU WKHȜÿé â¯ąœÏ¦ϭâéÞî’é ÈϘœϮѺ â¯ąœÏ¦ϭ¯ÈéϮѶ â¯ąœÏ¦ϭâéÞî’é ÈϘœ ώϮ ± QR PDWWHU ZKHWKHU ȜÿéLVAe::

UHIHUV WR D WDLO OLVW RI OHQJWK   RU DQ\ RWKHU QXPEHU

,IȜÿéZRXOG QRW EH D UHIHUHQFH W\SH EXW UDWKHU GHFODUHG DVâéÞî’é ÈϘœ Ȝÿé WKHQ WKH VL]H RI D QRGH ZRXOG EH XQGHILQHG GXH WR WKH VXP¶V GHILQLWLRQ EHFRPLQJ UHFXUVLYH â¯ąœÏ¦ϭâéÞî’é ÈϘœϮѺ â¯ąœÏ¦ϭ¯ÈéϮѶâ¯ąœÏ¦ϭâéÞî’é ÈϘœϮ :KHQ WKH SURJUDP DOORFDWHV VSDFH IRU D QRGH LW QHHGV WR NQRZ WKH VL]H RI D QRGH LQ E\WHV ,Q & GHILQLQJ D GDWD W\SH ZLWK VXFK D UHFXUVLYH VL]H GHILQLWLRQ LV IRU WKLV UHDVRQ SURKLELWHG

,Q FRQFOXVLRQ UHIHUHQFHV DUH XVHIXO IRU WKH FRQVWDQW VL]H WKH\ KDYH QR PDWWHU ZKDW WKH VL]H RI WKH UHIHUHQW LV WKLV NQRZOHGJH LV KHOSIXO WR LPSOHPHQW DV SUHVHQWHG UHFXUVLYH GDWD W\SHV 5HFXUVLYH GDWD W\SHV FRXOG EH LPSOHPHQWHG

,I ZH VTXLQW DQG ORRN DW G\QDPLFDOO\ VL]HG DUUD\V RI`HOHPHQWV DQG OHQJWKN DV WXSOHV RI D` YDOXH DQG DQ DUUD\ RI OHQJWKN − 1 ZH VHH WKDW WKH UHIHUHQFHV DUH DOVR JHQHUDOO\ QHFHVVDU\ IRU G\QDPLFDOO\ VL]HG DUUD\V MXVW OLNH RWKHU UHFXUVLYH GDWD W\SHV

:H DUH VNLSSLQJ RYHU GDWD VWUXFWXUH DOLJQPHQW LQ & IRU VLPSOLFLW\

(18)

ZLWKRXW SRLQWHUV EXW WKH LPSOHPHQWDWLRQV ZH DUH DZDUH RI HQG XS UHO\LQJ RQ D

IRUP RI UHIHUHQFHV OLNH LQWHJHU LQGLFHV LQWR DQ DUUD\ RI QRGHV

 5HIHUHQFHV )RU &RQVWDQW 7LPH 3DVVLQJ RI /DUJH 'DWD

7KHUH DUH DW OHDVW WZR UHDVRQV WR SDVV D UHIHUHQFH WR D SDUDPHWHU UDWKHU WKDQ D FRS\ RI WKH SDUDPHWHU

 ,W FDQ EH PRUH HIILFLHQW WR SDVV D UHIHUHQFH WR D ODUJH REMHFW DV D SDUDPHWHU WKDQ PDNLQJ DQ H[SHQVLYH FRS\

 SDVVLQJ D UHIHUHQFH WR DQ REMHFW DV D IXQFWLRQ SDUDPHWHU UDWKHU WKDQ D FRS\ FDQ EH XVHG WR OHW WKH IXQFWLRQ FKDQJH WKH REMHFW

3DVVLQJ YDOXHV E\ UHIHUHQFH LQ D KLJKOHYHO ODQJXDJH ZDV ILUVW LPSOHPHQWHG LQ WKH ODQJXDJH 3/, ,Q 3/, LW ZDV SRVVLEOH IRU SRLQWHUV WR UHIHU WR WKH ORFDWLRQ RI D VWDFN YDULDEOH DV ZHOO UHIHUULQJ WR KHDSDOORFDWHG GDWD

 5HIHUHQFHV )RU 6KDULQJ RI 0XWDEOH 6WDWH

5HIHUHQFHV DOORZ UHDFKLQJ WKH VDPH REMHFW IURP VHYHUDO RWKHU YDULDEOHV RU RE MHFWV :KHQ WKLV REMHFW KDSSHQV WR EH PXWDEOH FKDQJHV WR LW FDQ EH SHUFHLYHG WKURXJK DOO DOLDVHV

7KLV EHKDYLRXU JLYHV ULVH WR XVHIXO SURJUDPPLQJ LGLRPV OLNH LWHUDWRUV

’Á…ââ Zéޯȧ:¯âéAϘœ ϩ ÛÞ¯ù…éœ Zéޯȧ:¯âéAϘœ Ȝÿéϝ ÛÞ¯ù…éœ Zéޯȧ œÁœÇœÈéϝ ََн Ûî‘Á¯’ ùϯ˜ …ÁÁZéޯȧâ`ÏeÛۜÞϭϮ ϩ Zéޯȧ:¯âéAϘœ È Ѻ 鬯âϝ ˜Ï ϩ ÈϘœÁœÇœÈé Ѻ ÈϘœÁœÇœÈéϘéÏeÛۜÞϭϮϝ ‡ È Ѻ ÈϘȜÿéϝ Ϫ ú¬¯Áœ ϭ’îÞޜÈé َТ ÈîÁÁϮϝ Ϫ Ϫ ’Á…ââ Zéޯȧ:¯âé+éœÞ…éÏÞ ϩ ÛÞ¯ù…éœ Zéޯȧ:¯âéAϘœ ’îÞޜÈéAϘœϝ † Ûî‘Á¯’ Zéޯȧ §œéAœÿéϭϮ ϩََнϪ Ûî‘Á¯’ ùϯ˜ …˜ù…È’œϭϮ ϩََнϪ Ϫ 

(19)

,Q WKH H[DPSOH WKH ILHOG ’îÞޜÈéAϘœ GHILQHG DW † UDQJHV RYHU DOO WKH

QRGHV LQ WKH OLVW LI WKH …˜ù…È’œPHWKRG LV FDOOHG RIWHQ HQRXJK ,PSRUWDQWO\ WKH FRQWHQWV RI’îÞޜÈéAϘœLV D UHIHUHQFH WR D QRGH WKDW LV DOVR SDUW RI WKH OLVW

7KLV PHDQV WKDW WKH FKDQJHV FDXVHG WR WKH OLVW REMHFW DW‡ ZLOO DIIHFW WKH YDOXHV D OLVW LWHUDWRU UHWXUQV 7KLV LV D IRUP RI FRPPXQLFDWLRQ EHWZHHQ REMHFWV DQG LQWHQGHG EHKDYLRXU ,W LV SRVVLEOH GXH WR WKH XVH RI VKDUHG UHIHUHQFHV WR PXWDEOH VWDWH

5HIHUHQFLQJ D PXWDEOH REMHFW IURP VHYHUDO ILHOGV FDQ EH XVHIXO IRU DV\PSWRW LFDOO\ EHWWHU SHUIRUPDQFH PXWDWLQJ DQ REMHFW WKDW LV UHDFKDEOH IURP N RWKHU REMHFWV LQGLUHFWO\ FKDQJHV WKH EHKDYLRXU RI WKHVH RWKHU REMHFWV DV ZHOO²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

 8QLQWHQGHG 6KDULQJ RI 0XWDEOH 6WDWH

:KLOH UHIHUHQFHV DUH D SRZHUIXO FRQVWUXFW WKH\ DUH DOVR GDQJHURXV (YHQ WKH MXVWLILFDWLRQ IRU WKH FRPSXWHU SLRQHHU DZDUG DFNQRZOHGJHV WKDW TXRWH

³

:KHQ XWLOLVHG LQ D QRQSURIHVVLRQDO PDQQHU SRLQWHU YDULDEOHV KDYH OHG WR VRIWZDUH UHOLDELOLW\ SUREOHPV 7KHVH SUREOHPV DUH HYLGHQW LQ HQRUPRXV VRIWZDUH FRPSRVLWHV FRQWDLQLQJ VLJQLILFDQW XQQHFHVVDU\ FRPSOH[LW\

² ,((( &RPS 6RF >@

3URJUDPPHUV DUH WDVNHG ZLWK DYRLGLQJ WKHVH SUREOHPV QRW ODQJXDJHV DQG WRROV

³

%\ QRW SURSHUO\ HQJLQHHULQJ VRIWZDUH FRPSOH[ SRLQWHU UHODWLRQVKLSV DQG VWDWXV FDQ DULVH WKDW DUH GLIILFXOW WR SUHGLFW DQG WUDFH WKXV OHDGLQJ WR GLIILFXOWLHV :KHQ ZLOO ZH HYHU OHDUQ WKDW HQJLQHHULQJ GLVFLSOLQH LV UHTXLUHG WR SURGXFH KLJK TXDOLW\ VRIWZDUH" 3RLQWHU YDULDEOHV ZKHQ SURSHUO\ XWLOLVHG KDYH SURYLGHG KXQGUHGV RI WKRXVDQGV RI VRIWZDUH HQJLQHHUV ZLWK DQ HVVHQWLDO HQDEOLQJ WRRO RI WKH WUDGH

² ,((( &RPS 6RF >@

(20)

,W LV WUXH WKDW SRLQWHUV RU JHQHUDOO\ UHIHUHQFHV DUH ³DQ HVVHQWLDO HQDEOLQJ WRRO RI WKH WUDGH´ %XW WKH IDFW WKDW WKHLU XVH UHPDLQV DIWHU GHFDGHV RI LQGXVWU\ XVH D UHOLDELOLW\ SUREOHP PLJKW FRPH IURP WKH IDFW WKDW UHIHUHQFHV PDNH LW WRR HDV\ WR GR WKH ZURQJ WKLQJ UHIHUHQFHV FDQ E\ ZD\ RI DOLDVLQJ DQG PXWDELOLW\ LQWURGXFH D KLGGHQ FRQQHFWLRQ IURP RQH DJJUHJDWH REMHFW WR DQRWKHU LI D SUR JUDPPHU LV QRW DZDUH WKDW VXFK D FRQQHFWLRQ H[LVWV WKH\ FDQ HDVLO\²EHOLHYLQJ WKH\ DUH PRGLI\LQJ RQO\ RQH RI WKH REMHFWV²PRGLI\ ERWK RI WKHP 7KLV DFFL GHQWDO PRGLILFDWLRQ RI DQ REMHFW LV D EXJ DQG ILQGLQJ WKDW EXJ FDQ EH YHU\ KDUG DV LW PD\ QRW EH FOHDU ZKHUH FKDQJHV DUH FRPLQJ IURP $ SURJUDPPHU QHHGV WR XQGHUVWDQG DOLDVLQJ RI PXWDEOH VWDWH LQ RUGHU WR PRGLI\ D SURJUDP VKH KHUVHOI KDV QRW ZULWWHQ

$V DQ H[DPSOH FRQVLGHU D SURJUDP¶V PHPRU\ LQ )LJXUH D WKHUH DUH WZR VWDFN YDULDEOHVÛÏÞé¦ÏÁ¯Ï΀DQGÛÏÞé¦ÏÁ¯Ï΁WKDW FRQWDLQ WKH DGGUHVVHV RI GLI

IHUHQW REMHFWV +RZHYHU WKH WUDQVLWLYH FORVXUHV RI WKHVH REMHFWV DUH QRW GLVMRLQW ,Q SDUWLFXODU ZH FDQ UHDFK WKH REMHFW PDUNHG† IURP DQ REMHFW LQÛÏÞé¦ÏÁ¯Ï΀¶V

WUDQVLWLYH FORVXUH YLD WKH ILHOG¦ DQG DV ZHOO IURP DQ REMHFW LQÛÏÞé¦ÏÁ¯Ï΁¶V WUDQVLWLYH FORVXUH YLD WKH ILHOG§  $Q\ REMHFW ZH FDQ UHDFK IURP† OLNH WKH ‡ RE

MHFW LV WKHUHIRUH DOVR UHDFKDEOH IURP ERWKÛÏÞé¦ÏÁ¯Ï΀DQGÛÏÞé¦ÏÁ¯Ï΁ 7KHUH IRUH PRGLI\LQJ WKH GDWD UHDFKHG IURP ÛÏÞé¦ÏÁ¯Ï΀FDQ LQGLUHFWO\ FKDQJH WKH

VWDWH RIÛÏÞé¦ÏÁ¯Ï΁XQH[SHFWHGO\ DQG YLFHYHUVD 7KLV PD\ OHDG WR PHWKRGV

EHLQJ FDOOHG RQÛÏÞé¦ÏÁ¯Ï΁WKDW EUHDN LQYDULDQWV DVVRFLDWHG ZLWKÛÏÞé¦ÏÁ¯Ï΀ 7R XVH DQ H[DPSOH E\ +RJJ HW DO >@RI D FODVV PRGHOOLQJ SRUWIROLRV RI ILQDQ

FLDO DVVHWV WKDW FRQWDLQ FKHFNLQJ DFFRXQWV DQG SHUKDSV RWKHU DVVHWV  3RUWIROLRV KDYH WKHéޅÈ⦜Þ`ÏϭSÏÞé¦ÏÁ¯Ï Ï鬜Þϓ ¯Èé …ÇÏîÈéϮPHWKRG WKDW ZLOO WUDQV

IHU PRQH\ IURP RQH SRUWIROLR WR DQRWKHU &RQVLGHU WKH IROORZLQJ VWDWHPHQW

ÛÏÞé¦ÏÁ¯Ï΀ϘéޅÈ⦜Þ`ÏϭÛÏÞé¦ÏÁ¯Ï΁ϓ ΀ͿͿϮϝ

:LOO H[HFXWLQJ WKLV FRGH GHFUHDVH WKH DPRXQW RI PRQH\ LQÛÏÞé¦ÏÁ¯Ï΀" 7KLV GHSHQGV LI ÛÏÞé¦ÏÁ¯Ï΀ DQGÛÏÞé¦ÏÁ¯Ï΁ DUH DOLDVHV WKH VWDWHPHQW ZLOO QRW

KDYH WKH H[SHFWHG HIIHFW ,Q WKLV FDVH LW LV HDV\ WR JXDUG DJDLQVW WKH FKHFN

…ââœÞéϭÛÏÞé¦ÏÁ¯Ï΀ َТ ÛÏÞé¦ÏÁ¯Ï΁ϮZLOO SUHYHQW WKH SUREOHP IURP EUHDNLQJ DQ LQYDULDQW +RZHYHU ZKDW KDSSHQV LI WKH SRUWIROLRV DUH QRW WKH VDPH REMHFW EXW HDFK KDSSHQV WR FRQWDLQ WKH VDPH FKHFNLQJ DFFRXQW OLNH LQ )LJXUH D" 7KH EHKDYLRXU ZLOO EH HTXDOO\ XQH[SHFWHG EXW WKH VLPSOH G\QDPLF DVVHUWLRQ GRHV QRW VROYH WKH LVVXH DQ\ ORQJHU ,I WKH SRUWIROLR FODVV PDNHV LWV LQWHUQDO VWDWH LQDFFHVVLEOH E\ RXWVLGH FRGH WKH SUREOHP FDQ QR ORQJHU EH VROYHG ZLWKRXW PRGLI\LQJ WKH SRUWIROLR FODVV

,QVWHDG RI G\QDPLFDOO\ HQIRUFLQJ DOLDVLQJ LQYDULDQWV ZH FRXOG FRQVLGHU VWDWLF DQDO\VLV WR DYRLG XQLQWHQGHG VKDULQJ RI PXWDEOH VWDWH 3RLQWHU DQDO\VLV DQDO\ VLV RI ZKHWKHU RU QRW WZR SRLQWHUV PD\ UHIHU WR WKH VDPH REMHFW ZDV VKRZQ >  @ WR EH XQGHFLGDEOH²QR JHQHUDO DOJRULWKP H[LVWV WKDW FRPSXWHV SUHFLVHO\ ZKHWKHU RU QRW WZR SRLQWHU YDULDEOHVÿDQGĀPD\ FRQWDLQ WKH VDPH SRLQWHU DW

:H DUH WUDQVODWLQJ WKH FRGH WR D -DYDOLNH V\QWD[ IURP WKH RULJLQDO 6PDOOWDON FRGH

(21)

g f h portfolio1 p portfolio2 p … … … … D 8QLQWHQWHG VKDULQJ last first

E ,QWHQGHG VKDULQJ LQ D OLQNHG OLVW )LJXUH  3RLQWHUV FDQ EH XVHG IRU VKDULQJ D 3URJUDPPHUV PLJKW QRW NQRZ DERXW

WKHVH FRQQHFWLRQV EHWZHHQ PXWDEOH VWDWH WKHUHE\ FDXVLQJ EXJV E\ ILUVW ZULWLQJ WR WKH VWDWH UHDFKDEOH IURPÿDQG WKHQ UHDGLQJ IURP WKH VWDWH UHDFKDEOH IURPĀ RU YLFHYHUVD  E :KHQ VKDULQJ LV LQWHQGHG LW FDQ KDYH D SRVLWLYH HIIHFW OLNH DO(1) DGG RSHUDWLRQ LQ D OLQNHG OLVW WKDW QHHGV DÁ…âéSRLQWHU DQG WKHUHIRUH DOLDVLQJ

D JLYHQ ORFDWLRQ :H ZLOO EULHIO\ JLYH DQ LQWXLWLRQ IRU ZK\ WKLV LV WKH FDVH 5DPDOLQJDP >@ UHGXFHV DOLDVLQJ DQDO\VLV WR 3RVW¶V FRUUHVSRQGHQFH SUREOHP >@ ZKLFK LV NQRZQ WR EH XQGHFLGDEOH 7KH UHGXFWLRQ ZRUNV E\ REVHUYLQJ D

SURJUDP WKDW XVHV WZR SRLQWHUV p, q WR WUDYHUVH D ELQDU\ WUHH ,Q D ORRS WKH SUR JUDP FKRRVHV D UDQGRP LQWHJHU i DQG XVHV LW DV LQGH[ WR DFFHVV WR VHTXHQFHV RI LQWHJHUV w DQG z 7KH LQWHJHUV DUH LQWHUSUHWHG DV UHODWLYH GLUHFWLRQV LQ WKH WUHH HDFKͿLQ WKH LQWHJHU¶V ELQDU\ UHSUHVHQWDWLRQ FRUUHVSRQGV WR D OHIWVWHS HDFK΀

WR D ULJKWVWHS 7KH p SRLQWHU LV XSGDWHG XVLQJ WKH YDOXH GUDZQ IURP w WKH q SRLQWHU LV XSGDWHG XVLQJ D YDOXH GUDZQ IURP z

$W WKH HQG RI WKDW ORRS WKH SRLQWHUV PD\ DOLDV LII SRVW¶V FRUUHVSRQGHQFH SUREOHP KDV D VROXWLRQ IRU WKH VHTXHQFHV w1, . . . , wrDQG z1, . . . , zr

2EWDLQLQJ WKDW ³HQJLQHHULQJ GLVFLSOLQH´ WKDW SURJUDPPHUV DUH VXSSRVHGO\ VKRXOG KDYH LV QRW HDV\ ZH ZDQW WR FRQVHUYH WKH XVHIXO IHDWXUHV RI SRLQWHUV FKHDS SDVVLQJ RI GDWD G\QDPLFDOO\ VL]HG GDWD VWUXFWXUHV LQWHQGHG VKDULQJ  EXW ZH ZDQW WR SUHYHQW WKH EXJV FDXVHG E\ XQLQWHQGHG VKDULQJ

7R EDODQFH WKH TXRWH IURP EHIRUH ZH FDQ JLYH DQRWKHU TXRWH RQH WKDW LV DV KDUVK DV WKH SUHYLRXV TXRWH LV IRUJLYLQJ

³

5HIHUHQFHV DUH OLNH MXPSV OHDGLQJ ZLOGO\ IURP RQH SDUW RI D GDWD VWUXFWXUH WR DQRWKHU 7KHLU LQWURGXFWLRQ LQWR KLJK OHYHO ODQJXDJHV KDV EHHQ D VWHS EDFNZDUG IURP ZKLFK ZH PD\ QHYHU UHFRYHU

² &$% +RDUH >@

3RVW¶V &RUUHVSRQGHQFH 3UREOHP JLYHQ WZR VHTXHQFHV RI VWULQJVw

1, . . . , wNDQGz1, . . . , zN

RYHU VRPH DOSKDEHW GHFLGH ZKHWKHU RU QRW WKHUH LV QRQHPSW\ VHTXHQFH RI LQGLFHVi1, . . . , . . . , ir

VW WKH FRQFDWHQDWLRQVwi1· · · wir= zi1· · · zirDUH HTXDO

(22)

:KLOH XQLQWHQGHG VKDULQJ RI PXWDEOH GDWD LV FOHDUO\ SUREOHPDWLF ZH VRPH WLPHV LQWHQG WR WKHQ ZH RIWHQ ZDQW WR DYRLG FKDQJLQJ WKH GDWD WR QRW LQDGYHU WHQWO\ FKDQJH RWKHU SDUWV RI PHPRU\ LQGLUHFWO\ 7KH QH[W WZR VHFWLRQV JLYH D ELUGVH\H YLHZ LQ WKH IRUP RI FODVVLILFDWLRQ RI IHDWXUHV RI V\VWHPV WKDW UHVWULFW DOLDVLQJ DQG PXWDWLRQ $V D ELUGVH\H YLHZ XVXDOO\ GRHV WKH FODVVLILFDWLRQ LQ WKHVH WZR VHFWLRQV LV SDLQWLQJ LQ EURDG VWURNHV LW ZLOO FRPSDUH W\SHVDIH DE VWUDFWLRQV ZLWK SURJUDPPLQJ LGLRPV DQG OLEUDULHV XVHG LQ ORZ OHYHO SURJUDP PLQJ ODQJXDJHV ZKLFK XVXDOO\ KDYH IHDWXUHV WR GLVDEOH DOO VDIHW\ JXDUDQWHHV  7KH UHDVRQ WR LQWURGXFH WKLV FDWHJRU\ LV WR JLYH WKH UHDGHU D EDVLF XQGHUVWDQGLQJ RI PDQ\ RI WKH FRQFHSWV ZH ZLOO WDON DERXW

 5HVWULFWLQJ $OLDVLQJ $ 7D[RQRP\

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

7KH FDWHJRULHV WKDW ZH ZLOO XVH DUH

7KH PRGH RI DOLDV UHVWULFWLRQV $Q REMHFW FDQ EH VKDUHG ZKHQ PRUH WKDQ RQH

UHIHUHQFHV WR LW PD\ H[LVW  LW FDQ EH WHPSRUDULO\ VKDUHG ZKHQ WKH SUR JUDP¶V UXQWLPH LV GLYLGHG LQWR SKDVHV ZKHUH PRUH WKDQ RQH UHIHUHQFH WR DQ REMHFW H[LVW DOWHUQDWLQJ ZLWK SKDVHV ZKHUH WKHUH LV RQO\ RQH DOLDV  RU LW FDQ EH XQLTXH ZKHQ RQO\ RQH UHIHUHQFH WR LW H[LVWV  7HPSRUDU\ VKDU LQJ LV D WHFKQLTXH WKDW LV FRPPRQO\ XVHG WR SHUPLW XVHUV WR FDOO PHWKRGV RQ XQLTXHO\ UHIHUHQFHG REMHFWV FDOOLQJ WKH PHWKRG FUHDWHV DQ DOLDV UHI HUHQFH DYDLODEOH WKURXJK WKH PHWKRG¶V鬯âSDUDPHWHU %XW ZKHQ鬯â

LV ERUURZHG LQ RWKHU ZRUGV LW ZLOO QHYHU EH VWRUHG LQWR WKH KHDS > @ WKLV DOLDV RQO\ H[LVWV IRU WKH GXUDWLRQ RI WKH PHWKRG FDOO &DOOLQJ PHWK RGV RQ D XQLTXHO\ UHIHUHQFHG REMHFW ZRXOG UHTXLUH WKH FDOOHH UHIHUHQFH WR EH PDGH XQDYDLODEOH DW FDOO VLWH IRU LQVWDQFH E\ VHWWLQJ WKH UHIHUULQJ YDULDEOH WRÈîÁÁLQ WKH SURFHVV DQG SDVVLQJ WKH鬯âUHIHUHQFH EDFN WR WKH FDOOHU DV SDUW RI WKH UHWXUQ YDOXH

7KH UHDFK RI DOLDV UHVWULFWLRQV :KLOH WKH PRGH RI DOLDV UHVWULFWLRQV LV DERXW

WKH UHIHUHQFH V WR DQ REMHFW WKH UHDFK RI DOLDV UHVWULFWLRQV LV DERXW ZKDW LV NQRZQ DERXW WKH UHIHUHQFHV UHDG WUDQVLWLYHO\ IURP WKH REMHFW 7KLV LV 

(23)

D PHFKDQLVP WKDW LV XVHG WR SURWHFW WKH LQQHU VWDWH RI DQ REMHFW E\ SUH YHQWLQJ XQFRQWUROOHG RXWVLGH DFFHVV 7KH UHDFK RI DOLDV UHVWULFWLRQV FDQ EH VKDOORZ PHDQLQJ WKDW DW OHDVW VRPH UHIHUHQFHV UHDG IURP WKH REMHFW DUH JOREDOO\ VKDUHG WKH\ FDQ EH SDVVHG DQ\ZKHUH  RU LW FDQ EH GHHS PHDQLQJ WKDW WKH DFFHVV WR WKH REMHFW¶V LQQHU VWDWH LV UHVWULFWHG

7KH VFRSH RI DOLDV UHVWULFWLRQV $OLDV UHVWULFWLRQV FDQ DSSO\ WR D ZKROH SUR

JUDP PHDQLQJ WKDW WKHUH UHDOO\ LV RQO\ RQH UHIHUHQFH WR D FHUWDLQ REMHFW LQ DOO WKH SURJUDP 7KLV NLQG RI DOLDVLQJ UHVWULFWLRQ ZKLFK ZH FDOO JOREDO

DOLDV UHVWULFWLRQV FI JOREDO XQLTXHQHVV LQ 3DSHU ,  LV GHVLUDEOH ± EXW

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

7KH LGHD RI D VFRSH RI DOLDV UHVWULFWLRQV ZLOO EH LPSRUWDQW LQ 3DSHU , ZKLFK LQWURGXFHV D VWDWLF W\SH V\VWHPV WR H[SUHVV D ZLGH UDQJH RI ILQH DOLDVLQJ UDQJLQJ IURP JOREDO GHHS NLQGV RI DOLDVLQJ UHVWULFWLRQV WKH PRVW UHVWULFWLYH ± EXW VDIHVW WR JOREDOO\ VKDUHG WKH PRVW SHUPLVVLYH ± EXW OHDVW VDIH  VHH &KDSWHU  DQG 3DSHU ,

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

 )RUPV RI ,PPXWDELOLW\ $ 7D[RQRP\

$W D ILUVW JODQFH LW PLJKW VHHP OLNH LPPXWDELOLW\ KDV D VLPSOH DQG VLQJOH GHI LQLWLRQ +RZHYHU WKLV LV QRW VR WKH WHUP ³LPPXWDELOLW\´ FDQ UHIHU WR D ZLGH UDQJH RI VHPDQWLFV 7KLV VHFWLRQ JURXSV VHPDQWLFV RI LPPXWDELOLW\ ± LQIRU PDOO\ ± IRU WKH SXUSRVH RI XQGHUVWDQGLQJ GLIIHUHQFHV DQG VLPLODULWLHV RI WKLV ZLGH UDQJH 7KHVH IHDWXUHV DUH



%RWK WKHLU DQG RXU GHILQLWLRQV DUH LQIRUPDO 2XU DOLDVLQJ PRGHV FDQ EH FRPELQHG IXUWKHU ZLWK VFRSH DQG UHDFK WR \LHOG D FODVVLILFDWLRQ WKDW VXEVXPHV PRUH GLYHUVH WHFKQLTXHV

(24)

7DEOH  ([DPSOHV IRU IRUPV RI VKDOORZ DOLDV UHVWULFWLRQV :H ZLOO LQWURGXFH WKRVH V\VWHPV LQ &KDSWHU 

/RFDO *OREDO

6KDUHG

(QFDSVXODWHG REMHFWV DUH ORFDO WR REMHFWV UHDFKDEOH IURP WKH HQFDSVXODWLQJ REMHFW

& SRLQWHU& SRLQWHU-DYD UHIHUHQFH W\SH ILHOGVYDULDEOHV

7HPS 6KDUHG

&¶VޜâéÞ¯’éSRLQWHUV IRUFH D SURJUDPPHU WR XVH RQO\ WKH RQH UHVWULFWHG DOLDV WR DQ REMHFW DV ORQJ DV WKLV SRLQWHU LV DOLYH FI 6HFWLRQ 

$ GDWD VWUXFWXUH¶V VSLQH DQG WKH LWHUDWRU¶V ILHOG WKDW UHIHUHQFHV WKH FXUUHQW QRGH WHPSRUDU\ ZKHQ LWHUDWRUV KDYH D ERXQGHG OLIHWLPH DV LV FRPPRQ  ³6WDQGDUG´ XQLTXH UHIHUHQFHV ZLWK ERUURZLQJ FI 6HFWLRQ   8QLTXH 7KH VHW RI HOHPHQWILHOGV RI D VHW GDWD VWUXFWXUH PD\ QHYHU FRQWDLQ WKH VDPH UHIHUHQFH WZLFH /LQHDU W\SHV FI 6HFWLRQ  LPPXWDEOH GDWD UHDFKDEOH IURP WKHP LV VKDUHG >@ 

*OREDO XQLTXHQHVV FI &KDSWHU  3DSHU ,  LI H[SOLFLW DOLDVLQJ LV DYRLGHG DQG WKH UHIHUUHGWR REMHFW FRQWDLQV VKDUHG GDWD

7KH UHDFK RI LPPXWDELOLW\ ,PPXWDELOLW\ FDQ EH VKDOORZ DSSO\ WR WKH REMHFW

LWVHOI EXW QRW WR DOO UHIHUHQFHV VWRUHG E\ WKH REMHFW RU GHHS WKH REMHFW LWVHOI LV LPPXWDEOH DQG DOVR DOO REMHFWV UHDFKDEOH IURP LW 

7KH JUDQXODULW\ RI LPPXWDELOLW\ ,PPXWDELOLW\ FDQ PHDQ WKDW DQ REMHFW PD\

QRW EH PXWDWHG WKURXJK D VLQJOH UHIHUHQFH WR DQ REMHFW EXW WKURXJK RWKHU FRSLHV RI WKDW UHIHUHQFH  RU LW FDQ PHDQ WKDW DQ REMHFW PD\ QRW EH PXWDWHG LQ RWKHU ZRUGV WR DOO UHIHUHQFHV WR WKH REMHFW DUH UHIHUHQFH LPPXWDEOH  RU LW FDQ DSSO\ WR DOO LQVWDQFHV RI D W\SH :H VSHDN RI UHIHUHQFH REMHFW RU FODVV LPPXWDELOLW\

7KH PRGH RI LPPXWDELOLW\ ,PPXWDELOLW\ FDQ EH SHUPDQHQW HJ D SHUPD

QHQWO\ LPPXWDEOH REMHFW PD\ QHYHU EH PXWDWHG RQFH LW¶V FRQVWUXFWHG OLNH LQ SXUHO\ IXQFWLRQDO SURJUDPPLQJ RU WHPSRUDU\ HJ DQ REMHFW WKDW XQ GHUJRHV DQ LQLWLDOLVDWLRQ SKDVH DQG DW VRPH SRLQW ³IUHH]HV´ OLNH REMHFWV XVLQJ PHPRLVDWLRQ RU OD]\ LQLWLDOLVDWLRQ RU DQ REMHFW WKDW KDV FOHDUO\ GH OLQHDWHG SKDVHV LQ LWV OLIHWLPH GXULQJ ZKLFK LW ZRQ¶W EH PXWDWHG OLNH SDVV LQJ D & VWULQJ WR D IXQFWLRQ WKDW ZLOO ZULWH WR LW HJ IRU PDNLQJ D FRS\

âéޒÛĀϭ…Ϯ 

&RQVLGHULQJ WKH OLVW DERYH ZH VHH WKDW WKH WHUP ³LPPXWDELOLW\´ FDQ UHIHU WR D JUHDW YDULHW\ RI PHDQLQJV VRPH RI ZKLFK DUH YHU\ UHVWULFWLYH EXW PDLQWDLQ 

(25)

7DEOH  ([DPSOHV IRU IRUPV RI GHHS DOLDV UHVWULFWLRQV :H ZLOO LQWURGXFH WKRVH V\VWHPV LQ &KDSWHU 

/RFDO *OREDO

6KDUHG

)URP 3DSHU , 2EMHFW ZLWK QR§Áϑ…ÁGRPDLQ SDUDPHWHUV UHIHUHQFHG WKURXJK D VKDUHG GRPDLQ FI &KDSWHU  3DSHU , 

3RLQWHU WR -DYD&& REMHFW XVLQJ HQFDSVXODWLRQ

%ULGJH 2EMHFWV LQ ,VODQGV >@ 7HPS 6KDUHG

5XVW YDOXHV HQIRUFH WKDW WKHLU DOLDVHV QHYHU RXWOLYH WKH REMHFW DQG WKDW DQ\ UHIHUHQFHV WDNHQ IURP LQVLGH DQ REMHFW KDYH D OLIHWLPH VKRUWHU WKDQ WKH REMHFW GHHS  )URP 3DSHU , D XQLTXH UHIHUHQFH WKDW LV WHPSRUDULO\ DOLDVHG DQG ODWHU UHFRYHUHG WR XQLTXH FI &KDSWHU  3DSHU ,  %DOORRQ REMHFWV > @ VHH 6HFWLRQ  '\QDPLF ERUURZLQJ HJ 5XVW¶V âé˜َМ’œÁÁ>@ FI 6HFWLRQ  HQVXUHV WKDW WKH REMHFW LV DFFHVVHG WKURXJK RQO\ RQH RI WKH DOLDVHV DW D WLPH

0XWH[ORFNLQJ DFFHVVHV WR DQ REMHFW WKDW HQFDSVXODWHV LWV UHSUHVHQWDWLRQ HQVXUHV WKDW RQO\ RQH RI WKH UHIHUHQFHV PD\ DFFHVV WKH REMHFW DW HDFK WLPH

8QLTXH

)URP 3DSHU , ORFDO XQLTXHQHVV RI DQ REMHFW WKDW XVHV RQO\ JOREDOO\ XQLTXH W\SH SDUDPHWHUV FI &KDSWHU  3DSHU , 

7KHȜÿéILHOGV LQ D OLVW¶V VSLQH IRUP D VHW RI ILHOGV WKDW FRQWDLQV HDFK UHIHUHQFH RQO\ RQFH EXW DQ H[WHUQDO LWHUDWRU ZLOO FRQWDLQ DOLDVHV RI WKHȜÿéILHOGV

)URP 3DSHU , D JOREDOO\ XQLTXH UHIHUHQFH RI W\SH`ϗîȯÝîœ  ZKHUH`¶V W\SH SDUDPHWHUV DUH DOO JOREDOO\ XQLTXH FI &KDSWHU  3DSHU , DQG H[SOLFLW VKDULQJ LV DYRLGHG

VWURQJ LQYDULDQWV IRU UHDVRQLQJ DERXW SURJUDPV  DQG RWKHUV DUH YHU\ SHUPLVVLYH EXW PDLQWDLQ RQO\ ZHDN LQYDULDQWV 

7R LOOXVWUDWH KRZ ZH FDQ XVH WKHVH GLIIHUHQW NLQGV RI XQLTXHQHVV ZH¶OO FRQ GXFW D VPDOO OLWPXV WHVW ZKHWKHU UHRUGHULQJ WZR VWDWHPHQWV ZLOO SUHVHUYH WKH SURJUDP¶V PHDQLQJ RU QRW ,Q RWKHU ZRUGV ZH DVN ZKHWKHU WKHUH LV LQWHUIHU HQFH EHWZHHQ WKH WZR VWDWHPHQWV

…Ϙ¦ÏÏϭϮϝ ÿ Ѻ ‘Ϙ¦ϝ

'HILQLWLRQ  ,QWHUIHUHQFH EHWZHHQ VWDWHPHQWV 7ZR VWDWHPHQWV LQWHU

IHUH LI RQH RI WKHP ZULWHV GDWD WKDW WKH RWKHU UHDGV RU ZULWHV

(26)

shallow reference shallow object shallow class deep reference deep object

shallow referenceshallow objectshallow classdeep referencedeep objectdeep class

deep class             immutability of a immutability of b                                                         none none

)LJXUH  $VVXPLQJ WKH UHIHUHQFHV DUH LPPXWDEOH DW OHDVW WHPSRUDULO\ IRU WKH VFRSH

RI WKH FRGH VQLSSHW WKH DQVZHU GHSHQGV RQ ZKLFK NLQGV RI LPPXWDELOLWLHV WKH YDULDEOHV

…DQG‘KDYH UHRUGHULQJ SUHVHUYHV SURJUDP VHPDQWLFV

)LJXUH  VKRZV WKH UHVXOWV )RU H[DPSOH LI YDULDEOH…LV GHHSO\ UHIHUHQFH LPPXWDEOH GXULQJ WKH FRGH VQLSSHW WKDW LV VXIILFLHQW WR FRQFOXGH WKDW VHPDQ WLFV ZLOO QRW FKDQJH 7KLV LV EHFDXVH OLQH  FDQ QRW FKDQJH‘Ϙ¦ HYHQ WKRXJK WKH UHIHUHQFH LQ WKH YDULDEOH‘PLJKW EH LQFOXGHG VRPHZKHUH LQ…¶V WUDQVLWLYH

FORVXUH +RZHYHU WKDW WKH YDULDEOH ‘ LV GHHSO\ UHIHUHQFH LPPXWDEOH LV QRW

VXIILFLHQW D VLPSOH FRXQWHU H[DPSOH ZRXOG EH LI …DQG‘DUH DOLDVHV DQG WKH PHWKRG FDOO LQ OLQH  FKDQJHV WKH UHIHUHQFH VWRUHG LQ‘

7KHVH NLQGV RI LPPXWDELOLW\ DUH XVHG LQ SUDFWLFH EH LW LQ WKH IRUP RI W\SH DE VWUDFWLRQV DEVWUDFWLRQV SURYLGHG E\ OLEUDULHV RU VLPSO\ FRGLQJ LGLRPV (J RQ WKH UHVWULFWLYH VLGH ZH KDYH SHUPDQHQW GHHS FODVV LPPXWDELOLW\ OLNH LQ SXUHO\ IXQFWLRQDO GDWD VWUXFWXUHV FI 6HFWLRQ  2Q WKH OHDVW UHVWULFWLYH VLGH ZH KDYH WHPSRUDU\ VKDOORZ UHIHUHQFH LPPXWDELOLW\ OLNH &¶V’ÏÈâéSRLQWHUV >@ 7KH RYHUYLHZV LQ 7DEOH  DQG 7DEOH  VKRZ VRPH FRPPRQ XVH FDVHV DQG LPSOHPHQWDWLRQV RI WKH FRPELQDWLRQV RI WKH NLQGV RI LPPXWDELOLW\ ZH FDQ H[ SUHVV LQ WKH FODVVLILFDWLRQ IURP WKLV VHFWLRQ :H ZLOO VWDUWLQJ ZLWK &KDSWHU  JR WKURXJK WKHVH V\VWHPV DQG H[SODLQ WKHP RQH E\ RQH ,Q &KDSWHU  ZH ZLOO WDON DERXW KRZ FRPPRQO\ XVHG VRPH RI WKHVH NLQGV RI LPPXWDELOLW\ DUH LQ SUDFWLVH

1RZ WKDW ZH KDYH GHPRQVWUDWHG ZKDW DOLDVLQJ LV KRZ LW LV SUREOHPDWLF ZKHQ PXWDEOH VWDWH LV DOLDVHG DQG ZKDW ZD\V WR PLWLJDWH WKH SUREOHPV DUH ZH DUH UHDG\ WR VXUYH\ VRPH PHDQV RI DOLDV FRQWURO WKDW KDYH EHHQ GHVLJQHG E\ SUDF WLWLRQHUV DV ZHOO DV UHVHDUFKHUV

(27)

7DEOH  'LIIHUHQW IRUPV RI VKDOORZ LPPXWDELOLW\ DQG H[DPSOHV WKH H[DPSOHV DUH QRW H[KDXVWLYH IRU ZKHUH WKH\ DUH XVHG :H ZLOO LQWURGXFH WKRVH V\VWHPV LQ &KDSWHU 

5HIHUHQFH 2EMHFW &ODVV

3HUPDQHQW

7KH UHIHUHQFHV D FROOHFWLRQ KDV WR LWV HOHPHQWV DUH XVXDOO\ QRW XVHG IRU PXWDWLRQ &&’ÏÈâéSRLQWHU ZKHQ WKH UHIHUHQW PD\ EH’ÏÈâé &DVWLQJ FRQVWQHVV DZD\ DQG PRGLI\LQJ WKH REMHFW ZRXOG WKHQ EH LOOHJDO >@ FI 6HFWLRQ   &RQVW YDOXHV ’ÏÈâé ` 6HFWLRQ   $ SRLQWHU WKDW LV ERWK XQLTXH DQG D UHDGRQO\ UHIHUHQFH FI 6HFWLRQ   & îȯÝîœϠÛéÞѽ’ÏÈâé `Ѽ ³XQLTXH SRLQWHU WR ’ÏÈâé´ 6HFWLRQ  

&& VWUXFW ZLWK RQO\ ’ÏÈâéILHOGV RU -DYD FODVV ZLWK RQO\¦¯È…Á ILHOGV ,PPXWDEOH FROOHFWLRQV RU RSWLRQ W\SHV ZKHQ WKH\ FRQWDLQ PXWDEOH GDWD FI ³FRQGLWLRQDO GHHS LPPXWDELOLW\´ 6HFWLRQ   7HPSRUDU\ &&’ÏÈâéSRLQWHUV WR D QRQFRQVW REMHFW WKHQ FRQVWQHVV FDQ EH W\SHFDVWHG DZD\ 6HFWLRQ   -DYD¶V XQPRGLILDEOH FROOHFWLRQV ZKHQ WKHUH DUH UHIHUHQFHV WR WKH LQQHU FROOHFWLRQ OHIW 6HFWLRQ   )UHH]LQJ D -DYD FROOHFWLRQ E\ PRYLQJ 'HILQLWLRQ  LW LQWR DQ XQPRGLILDEOH FROOHFWLRQ FI 6HFWLRQ   ² 

(28)

7DEOH  'LIIHUHQW IRUPV RI GHHS LPPXWDELOLW\ DQG H[DPSOHV QRW H[KDXVWLYH IRU ZKHUH WKH\ DUH XVHG :H ZLOO LQWURGXFH WKRVH V\VWHPV LQ &KDSWHU 

5HIHUHQFH 2EMHFW &ODVV

3HUPDQHQW -DYDUL UHDGRQO\ UHIHUHQFHV VHH 6HFWLRQ   ’ÏÈâé ` QRQSRLQWHU W\SH VHH 6HFWLRQ  LQ & LI` HQFDSVXODWHV LWV UHDFKDEOH VWDWH $ SHUPDQHQW UHDGRQO\ UHIHUHQFH WKDW LV NQRZQ WR EH XQLTXH FI 6HFWLRQ  &ÛÞÏۅ§…éœϠ’ÏÈâé ѽîȯÝîœϠÛéÞѽ’ÏÈâé ` ѼѼSRLQWHU VHH 6HFWLRQ  LI` HQFDSVXODWHV WKH UHDFKDEOH VWDWH RU XVHV ÛÞÏۅ§…éœϠ’ÏÈâéDV ZHOO ,PPXWDEOH GDWD VWUXFWXUHV HJ >@  -DYDULޜ…˜ÏÈÁĀFODVV VHH 6HFWLRQ   7HPSRUDU\ &` ’ÏÈâé ώ VHH 6HFWLRQ   LI WKH W\SH`HQFDSVXODWHV LWV UHDFKDEOH VWDWH ,I WKH UHIHUHQW LV QRW DFWXDOO\ ’ÏÈâé LW FDQ EH W\SHFDVWHG WR` ώ 5XVW REMHFWV DUH LPPXWDEOH GXULQJ SHULRGV RI DOLDVLQJ )UDFWLRQDO SHUPLVVLRQV 6HFWLRQ   /D]LO\ LQLWLDOLVHG FODVVHV &ODVVHV ZLWK FDFKLQJ HJ MDYD VWULQJV WKDW FDFKH WKH UHVXOW RI WKH ¬…â¬ϘœPHWKRG  

(29)

 /DQJXDJH $EVWUDFWLRQV IRU $OLDV &RQWURO

7KH ELJ OLH RI REMHFWRULHQWHG SURJUDPPLQJ LV WKDW REMHFWV SURYLGH HQFDSVXODWLRQ

- +RJJ >@

$OLDVLQJ RI PXWDEOH VWDWH LV D GRXEOHHGJHG VZRUG 2Q WKH RQH KDQG LW FDQ VXSSRUW XVHIXO SURJUDPPLQJ LGLRPV 6HFWLRQ   2Q WKH RWKHU KDQG LW FDQ OHDG WR EXJV EHFDXVH KRZ IDU DQ REMHFW LV VKDUHG LV QRW DOZD\V FOHDU

$OLDV FRQWURO 'HILQLWLRQ   URXJKO\ LV WKH DWWHPSW WR H[SUHVV LQ D SURJUDP KRZ DQG ZKHWKHU REMHFWV FDQ EH DOLDVHG DQG RIWHQ LQFOXGHV SURWRFROV WKDW PD\ LQFOXGH DGGLWLRQDO FRQVWUDLQWV RQ WKH XVH RI DOLDVHG GDWD UHODWHG WR PXWDWLRQ RI DOLDVHG GDWD

'HILQLWLRQ  $OLDV FRQWURO 7KH WHUP DOLDV FRQWURO ZDV FRLQHG E\ +RJJ

HW DO >@ $OLDV FRQWURO JURXSV WHFKQLTXHV WKDW SHUPLW DOLDVLQJ WR KDSSHQ EXW GR VR LQ D ZD\ WKDW SHUPLWV D SURJUDPPHU WR WHOO ZKHQ WKLV LV WKH FDVH $OLDVLQJ FRQWURO DLGV SURJUDPPHUV WR HQVXUH WKDW XQH[SHFWHG DOLDVLQJ ZLOO QHYHU RFFXU

,Q WKH QH[W VHFWLRQ 6HFWLRQ  ZH ZLOO VXUYH\ WHFKQLTXHV WKDW OHW D SUR JUDPPHU DYRLG RU PDNH WKHP H[SOLFLW LQ FRGH LQ D ZD\ WKDW LV VXLWDEOH WR DYRLG EXJV FDXVHG E\ XQLQWHQWLRQDO DOLDVLQJ $IWHU LQ 6HFWLRQ  ZH ZLOO FRYHU VRPH WHFKQLTXHV WKDW DUH DYDLODEOH WR UHVWULFW LQVWHDG WKH PRGLILFDWLRQ RI GDWD LQ RUGHU WR VDIHO\ VKDUH GDWD

 5HVWULFWLQJ $OLDVLQJ

7KHUH DUH WZR REYLRXV VROXWLRQV WR DYRLG SUREOHPV FDXVHG E\ DOLDVLQJ RI PXWD EOH VWDWH WR UHVWULFW DOLDVLQJ RI PXWDEOH GDWD RU WR UHVWULFW PXWDWLRQ RI DOLDVHG GDWD E\ XVLQJ IRUPV RI LPPXWDELOLW\ 7KLV VHFWLRQ FRYHUV WKH ILUVW WR UHVWULFW DOLDVLQJ ZKLOH 6HFWLRQ  FRYHUV WKH ODWWHU

:H ZLOO VWDUW ZLWK HQFDSVXODWLRQ D SDWWHUQ WKDW LV ZLGHO\ XVHG LQ REMHFW RUL HQWHG SURJUDPPLQJ DQG LWV OLPLWDWLRQV :H ZLOO FRQWLQXH ZLWK W\SH V\VWHPV WKDW DUH GHVLJQHG WR FRQWURO SUHFLVHO\ KRZ UHIHUHQFHV FDQ EH DOLDVHG LQ RUGHU WR JLYH PRUH UHOLDEOH PHDQV RI XQGHUVWDQGLQJ FRGH WKDQ WRGD\¶V PDLQVWUHDP SURJUDPPLQJ ODQJXDJHV

(30)

o o'

×

)LJXUH  2EMHFW o HQFDSVXODWHV 'HILQLWLRQ  WKH REMHFWV GUDZQ ZLWKLQ WKH EXEEOH

LQFOXGLQJ REMHFW o $V oLV HQFDSVXODWHG UHIHUHQFHV IURP WKH RXWVLGH OLNH WKH FURVVHG UHIHUHQFH DUH SUHYHQWHG 7KH REMHFW UHDFKDEOH GLUHFWO\ IURP o LV QRW HQFDSVXODWHG LQVLGH o DV WKHUH LV D SDWK RI UHIHUHQFHV WR LW WKDW GRHV QRW JR WKURXJK o

 (QFDSVXODWLRQ RI 0XWDEOH 6WDWH

2QH WKH PRVW ZHOO NQRZQ WHFKQLTXHV WR UHVWULFW DOLDVLQJ LQ SURJUDPPLQJ SUDF WLFH LV HQFDSVXODWLRQ 'HILQLWLRQ   )LJXUH  VKRZV D SDUWLDO REMHFW JUDSK ZKHUH DQ REMHFW o HQFDSVXODWHV VHYHUDO REMHFWV WKDW DUH WUDQVLWLYHO\ UHDFKDEOH

'HILQLWLRQ  (QFDSVXODWLRQ $Q REMHFW o HQFDSVXODWHV DQRWKHU REMHFW o

DV ORQJ DV oFDQ RQO\ EH DFFHVVHG GXULQJ PHWKRG FDOOV WR REMHFW o 7KLV GHILQLWLRQ RI HQFDSVXODWLRQ LV DERXW UHDFKDELOLW\ RI GDWD XQOLNH VRPH GHI LQLWLRQV RI WKH VDPH WHUP LQ WKH FRQWH[W RI REMHFW RULHQWHG SURJUDPPLQJ

(QFDSVXODWLRQ LV 'LIILFXOW WR ,PSOHPHQW

$ SUREOHP ZLWK HQFDSVXODWLRQ LV WKDW LW LV KDUG WR HQIRUFH FRQVLVWHQWO\ &RQ VLGHU WKH IROORZLQJ FODVV RI ILQDQFLDO SRUWIROLRV WKDW ZH KDYH DOUHDG\ XVHG DV DQ H[DPSOH LQ 6HFWLRQ  $ UHDVRQDEOH LQYDULDQW LV WKDW D SRUWIROLR PXVW DO ZD\V HQFDSVXODWH WKH FKHFNLQJ DFFRXQW ZLWKLQ LW VXFK WKDW QR RXWVLGH FRGH FDQ DFFHVV WKH FKHFNLQJ DFFRXQW GLUHFWO\ 7KLV PDNHV HQFDSVXODWLRQ D GHHS IRUP RI DOLDV UHVWULFWLRQ ΀ Ûî‘Á¯’ × ’Á…ââ SÏÞé¦ÏÁ¯Ï ϩ ΁ ÛÞÏ霒霘 ’’ÏîÈé …’’ϝ ΂ Ûî‘Á¯’ ’’ÏîÈé §œé’’ϭϮ ϩ ޜéîÞÈ é¬¯âϘ…’’ϝ × Ϫ ΃ Ûî‘Á¯’ ùϯ˜ âœé’’ϭ’’ÏîÈé …Ϯ ϩ 鬯âϘ…’’ Ѻ …ϝ × Ϫ ΄ Ϫ

7KLV VQLSSHW FRQWDLQV VHYHUDO YLRODWLRQV RI HQFDSVXODWLRQ SDVVLQJ GDWD WR WKH RXWVLGH SDVVLQJ GDWD WR WKH LQVLGH DQG SULYLOHJHG DFFHVV WKURXJK LQKHULWDQFH :H QRZ JR WKURXJK WKHVH LQ RUGHU

3DVVLQJ 'DWD WR WKH 2XWVLGH

)LUVW WKH JHWWHU LQ OLQH  YLRODWHV HQFDSVXODWLRQ WKH§œé’’PHWKRG PXVW QRW

UHWXUQ WKH REMHFW UHIHUHQFHG E\ WKH…’’ILHOG²RU RWKHUZLVH RXWVLGH FRGH FRXOG 

(31)

FDOOÛÏÞé¦ÏÁ¯ÏϘ§œé’’ϭϮϘú¯é¬˜Þ…úϭϮZLWKRXW JRLQJ WKURXJK WKH SRUWIROLR LP

SOHPHQWDWLRQ 7KH JHWWHU FRXOG LQVWHDG UHWXUQ D FRS\ RI WKH DFFRXQW LQVWHDG

ޜéîÞÈ é¬¯âϘ…’’Ϙ’ÏÛĀϭϮ 2WKHU RSWLRQV ZRXOG EH WR LI WKH ODQJXDJHV KDV

WKDW IHDWXUH UHWXUQ D UHDGRQO\ UHIHUHQFH WR WKH DFFRXQW 6HFWLRQ   RU PRYH WKH DFFRXQW RXW RI WKH SRUWIROLR E\ VHWWLQJ WKH DFFRXQW ILHOG WRÈîÁÁEHIRUH UH

WXUQLQJ WKH DFFRXQW

3DVVLQJ 'DWD WR WKH ,QVLGH

6HFRQG WKH VHWWHU LQ OLQH  LV EURNHQ FOLHQW FRGH FRXOG LQVWDOO D FKHFNLQJ DF FRXQW UHWDLQ D UHIHUHQFH WR LW DQG XVH LW ODWHU WR ZLWKGUDZ PRQH\

’’ÏîÈé …’’ Ѻ Ȝú ’’ÏîÈéϭϮϝ

âÏǜSÏÞé¦ÏÁ¯ÏϘâœé¬œ’¾¯È§’’ÏîÈéϭ…’’Ϯϝ   DIWHU SRUWIROLR RZQHU KDV SXW PRQH\ LQ  …’’Ϙú¯é¬˜Þ…úϭϮϝ

,QVWHDG WKH DFFRXQW FRXOG XVH D FRS\ RI WKHȜú’’WKDW LV SDVVHG LQ鬯âϘ …’’ Ѻ Ȝú’’Ϙ’ÏÛĀϭϮ

3ULYLOHJHG $FFHVV 7KURXJK ,QKHULWDQFH

7KLUG WKH FODVV LV QRW PDUNHG¦¯È…ÁLQ OLQH  PHDQLQJ LW FDQ EH LQKHULWHG IURP HYHQ DIWHU WKH SÏÞé¦ÏÁ¯ÏFODVV LV IL[HG E\ FRS\LQJ WKH DFFRXQW HYHU\ WLPH LW

FURVVHV WKH HQFDSVXODWLRQ ERXQGDU\ FDUHOHVV XVDJH RI LQKHULWDQFH FDQ EUHDN HQFDSVXODWLRQ RQFH DJDLQ Ûî‘Á¯’ ’Á…ââ ÞϾœÈSÏÞé¦ÏÁ¯Ï œÿéœÈ˜â SÏÞé¦ÏÁ¯Ï ϩ ֞GùœÞÞ¯˜œ Ûî‘Á¯’ ’’ÏîÈé §œé’’ ϩ ޜéîÞÈ é¬¯âϘ…’’ϝ × Ϫ  VLPLODU IRU VHW$FF Ϫ

1RWH WKDW QRW HYHQ SUHYHQWLQJ WKH VXEFODVV IURP DFFHVVLQJ WKH…’’ILHOG E\

PDNLQJ LWÛÞ¯ù…éœ ZRXOG SUHYHQW LQKHULWDQFH IURP FDXVLQJ D SUREOHP DV ZH FRXOG VLPSO\ DGG D QHZ DFFRXQW ILHOG LQ WKH VXEFODVV DQG RYHUULGH WKH VHWWHU DV ZHOO DV WKH JHWWHU WR XVH WKDW QHZ ILHOG LQVWHDG

7KLV OLVW RI SUREOHPV LV QRW H[KDXVWLYH EXW VKRZV WKDW HYHQ IRU D VLQJOH

DQG VLPSOH FODVV HQIRUFLQJ DOLDVLQJ LQWHQWLRQV LV VXUSULVLQJO\ KDUG DQG ± ZKHQ FORQLQJ LV XVHG ± FRVWO\ $OVR LPSRUWDQWO\ UHDGLQJ WKH FRGH LV KDUG DV ZHOO WKH IDFW WKDW HQFDSVXODWLRQ LV SUHVHQW LV QHYHU VDLG H[SOLFLWO\ $OLDV FRQWURO LQ PDLQVWUHDP ODQJXDJHV LV RIWHQ SDLQWHG LQ WKH QHJDWLYH VSDFH²E\ FDUHIXOO\ RPLWWLQJ WKLQJV QRW E\ H[SOLFLWO\ VWDWLQJ ,Q WKH QH[W VHFWLRQ ZH ZLOO VHH V\V WHPV WKDW FDQ KHOS SURJUDPPHUV HQIRUFH SURSHUWLHV VXFK DV HQFDSVXODWLRQ LQ D PRUH UHOLDEOH PDQQHU E\ VWDWLQJ WKH SURSHUWLHV SRVLWLYHO\ UDWKHU WKDQ E\ RPLV VLRQ

ZH FRXOG IRU LQVWDQFH DOVR XVH -DYD¶V UHIOHFWLRQ WR PDNH WKH…’’ÏîÈéILHOG SXEOLF

(32)

 $OLDV &RQWURO E\ 6XEGLYLVLRQV RI WKH +HDS

2QH ZD\ WR OHW SURJUDPPHUV GHQRWH H[SOLFLWO\ KRZ PXFK DOLDVLQJ LV SRVVLEOH LV WR GLYLGH WKH KHDS LQWR GLVMRLQW UHJLRQV RI GDWD E\ XVLQJ D W\SH V\VWHP (DFK REMHFW OLYHV LQVLGH H[DFWO\ RQH UHJLRQ DQG XVXDOO\ WKLV LV DQ REMHFW SURSHUW\ DOO UHIHUHQFHV WR WKH REMHFW DJUHH  0RVW FRPPRQO\ WKHVH UHJLRQV DUH GHILQHG E\ REMHFWV OLNH WKH SRUWIROLR LQ 6HFWLRQ  DQ REMHFW FRXOG GHILQH WKDW ± IRU LQVWDQFH ± HYHU\ REMHFW UHDFKDEOH IURP LW LV FRQVLGHUHG WR EH LQVLGH LW DQG WKHUH IRUH DQ DOLDV FDQ QRW EH SDVVHG WR WKH RXWVLGH VLPLODUO\ QR RXWVLGH UHIHUHQFH FDQ EH VLPSO\ FRSLHG WR WKH LQVLGH ZLWKRXW PDNLQJ VXUH WKDW WKDW WKHUH DUH QR RXWVLGH DOLDVHV OHIW

%\ ORRNLQJ DW WKH UHJLRQ D UHIHUHQFH UHIHUV LQWR ZH FDQ RIWHQ UXOH RXW DOLDV LQJ LI WZR UHIHUHQFHV UHIHU WR REMHFWV LQ GLIIHUHQW UHJLRQV WKH\ PD\ QRW EH DOLDVHV EXW WZR UHIHUHQFHV UHIHUULQJ WR REMHFWV LQ WKH VDPH UHJLRQ PD\ EH DOLDVHV ,Q VXFK D V\VWHP D W\SH XVXDOO\ FDUULHV LQIRUPDWLRQ DERXW ZKLFK UH JLRQV RI PHPRU\ WKH REMHFWV WKDW DUH LQGLUHFWO\ UHIHUUHG WR IURP LW 'HILQLWLRQ  DUH LQ

'HILQLWLRQ  ,QGLUHFW 5HIHUHQFH $ UHIHUHQFH r LV DQ LQGLUHFW UHIHUHQFH

WR DQ REMHFW o LI WKHUH LV D QRQHPSW\ FKDLQ RI DFFHVVHV r.f1. . . fn WKDW

HYDOXDWHV WR o ,I WZR YDULDEOHV FRQWDLQ WKHVH UHIHUHQFHV ZH DOVR FDOO WKH YDULDEOHV LQGLUHFW UHIHUHQFHV WR o

%\ UHDVRQLQJ DERXW WKH UHJLRQV RI PHPRU\ WKDW DUH WUDQVLWLYHO\ UHDFKDEOH IURP WZR REMHFWV ZH FDQ RIWHQ LQIHU WKHUH FDQ EH QR LQGLUHFW DOLDVLQJ 'HILQL WLRQ  

'HILQLWLRQ  ,QGLUHFW $OLDVLQJ 7ZR UHIHUHQFHV r s DUH LQGLUHFWO\

DOLDVHG LI WKHUH H[LVWV DW OHDVW RQH REMHFW o VXFK WKDW ERWK r DQG s DUH LQGLUHFW UHIHUHQFHV WR o LQ RWKHU ZRUGV LI WKH WUDQVLWLYH FORVXUHV RYHU ODS ,I WZR YDULDEOHV ÿDQGĀFRQWDLQ WKHVH UHIHUHQFHV ZH DOVR FDOO WKH YDULDEOHV LQGLUHFW DOLDVHV 7KH YDULDEOHVÛÏÞé¦ÏÁ¯Ï΀DQGÛÏÞé¦ÏÁ¯Ï΁LQ )LJXUH D DUH LQGLUHFW DOLDVHV EHFDXVH WKH\ DUH ERWK LQGLUHFW UHIHUHQFHV WR WKH REMHFWV† DQG ‡

:H ZLOO SURYLGH DQ RYHUYLHZ RI WKLV ILHOG DQG PDNH DQ DWWHPSW WR EULQJ RXW VRPH LPSRUWDQW VLPLODULWLHV DQG GLIIHUHQFHV RI WKH ZRUN ZH SUHVHQW

,VODQGV DQG %DOORRQV 5HOLDEOH (QFDSVXODWLRQ

,VODQGV D SURSRVDO E\ +RJJ >@ LQWURGXFH WKH LGHD WR HQIRUFH HQFDSVXODWLRQ 'HILQLWLRQ  DW D ODQJXDJH OHYHO $Q LVODQG LV D UHJLRQ RI WKH KHDS WKDW FRQWDLQV DOO REMHFWV UHDFKDEOH IURP D EULGJH REMHFW ,Q RUGHU WR PRGLI\ WKH REMHFWV ZLWKLQ DQ LVODQG RQH PXVW FDOO PHWKRGV RQ WKH EULGJH REMHFW

(33)

p1 p p2

D 9DOLG LVODQGV DQG EDOORRQV

p1 p p2

E 9DOLG LVODQGV QRW EDOORRQV

)LJXUH  %ULGJH REMHFWV LQ LVODQGV FDQ EH DOLDVHG EXW QRW LQ EDOORRQV

)URP D IUHVKO\ DOORFDWHG REMHFW QR RWKHU REMHFWV FDQ EH UHDFKHG²D IUHVKO\ DOORFDWHG REMHFW WKHUHIRUH LV D EULGJH REMHFW UHSUHVHQWLQJ DQ HPSW\ LVODQG DV LW ZDV MXVW GHVFULEHG ,Q RUGHU WR PDLQWDLQ HQFDSVXODWLRQ +RJJ¶V ZRUN DGGL WLRQDOO\ GHPDQGV VRPH SURSHUWLHV RI EULGJH REMHFWV $V EULGJH REMHFWV DUH WKH HQWU\ SRLQWV LQWR D GLVMRLQW UHJLRQ RI PHPRU\ E\ HQVXULQJ WKDW

D RQO\ XQDOLDVHG UHIHUHQFHV JHW SDVVHG LQVLGH D EULGJH REMHFW LQFOXGLQJ GXULQJ WKH REMHFW FRQVWUXFWRU  DQG WKDW

E QR UHIHUHQFHV WR WKH LQWHUQDO UHSUHVHQWDWLRQ DUH FRSLHG RXWVLGH WKH EULGJH REMHFW

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

&RPLQJ EDFN WR WKH SRUWIROLR FODVV ZH WDONHG DERXW LQ 6HFWLRQ  DQG 6HFWLRQ  ZH FDQ QRZ VKRZ KRZ WKLV FODVV FRXOG EH LPSOHPHQWHG XVLQJ LVODQGV ZH XVH -DYDOLNH V\QWD[ IRU FRQVLVWHQW SUHVHQWDWLRQ 

Ûî‘Á¯’ ‘Þ¯˜§œ ’Á…ââ +âÁ…ȘâSÏÞé¦ÏÁ¯Ï ϩ ÛÞÏ霒霘 ’’ÏîÈé …’’ϝ

Ûî‘Á¯’ ֞eȯÝîœ ’’ÏîÈé §œé’’ϭϮ ϩ ޜéîÞÈ é¬¯âϘ…’’Ϙ’ÁÏȜϭϮϝ Ϫ Ûî‘Á¯’ ùϯ˜ âœé’’ϭ֞eȯÝîœ ’’ÏîÈé …Ϯ ϩ 鬯âϘ…’’ Ѻ ÇÏùœ …ϝ Ϫ

Ϫ

7KH LVODQG FODVV PD\ UHWXUQ RQO\ XQLTXH UHIHUHQFHV DQG DFFHSW RQO\ XQLTXH UHIHUHQFHV DV SDUDPHWHUV WR LWV PHWKRGV ERWK PDGH H[SOLFLW LQ WKH JHWWHU E\ XVLQJ DQ֞eȯÝîœDQQRWDWLRQ WKDW GHQRWHV D JOREDOO\ GHHSO\ XQLTXH UHIHUHQFH 

$VVXPLQJ WKH DFFRXQW KDV D’ÁÏȜ PHWKRG WKDW UHWXUQV D XQLTXH DFFRXQW UHI HUHQFH DV LW UHWXUQV D IUHVKO\ DOORFDWHG REMHFW  ZH FDQ HQIRUFH WKDW WKH JHWWHU



5HIHUHQFHV WR GHHSO\ REMHFW LPPXWDEOH GDWD FDQ DOVR FURVV WKURXJK EULGJH REMHFWV HYHQ ZKHQ DOLDVHG EXW ZH ZLOO IRFXV RQ WKH DOLDVLQJ SDUW RI WKH V\VWHP KHUH

(34)

UHWXUQV DQ DFWXDO FORQH WR WKH RXWVLGH 6LPLODUO\ WKH IDFW WKDW ZH RQO\ DFFHSW D XQLTXH UHIHUHQFH WR DQ DFFRXQW LQ WKHâœé’’PHWKRG IRUFHV D FOLHQW WR JLYH XS LWV RZQ UHIHUHQFH WR WKH DFFRXQW 7KHÇÏùœNH\ZRUG LV UHTXLUHG WR UHDG D

XQLTXH UHIHUHQFH LW H[SUHVVHV WKDW DV D VLGH HIIHFW RI UHDGLQJ WKH UHIHUHQFH LQ

… WKH YDULDEOH LV EHLQJ VHW WRÈîÁÁLQ RUGHU WR PDLQWDLQ XQLTXHQHVV VHH 6HF

WLRQ  

7KH LVODQGV ZRUN IHDWXUHV WZR LPSRUWDQW FRQFHSWV DV ODQJXDJH DEVWUDFWLRQV ± 7KH QRWLRQ RI QHVWHG UHJLRQV DQ LVODQG FDQ FRQWDLQ UHIHUHQFHV WR EULGJH

REMHFWV GHVFULELQJ D GHHSO\ VWUXFWXUHG SURJUDP PHPRU\

± 8QLTXH UHIHUHQFHV LQ RUGHU WR HQIRUFH UXOHV D DQG E DERYH LVODQGV UHTXLUH FRQVLVWHQW XVH RI XQLTXH UHIHUHQFHV IRU DOO SDUDPHWHU W\SHV DQG PHWKRG UHWXUQ W\SHV

7KH LVODQGV V\VWHP UHTXLUHV DQQRWDWLRQV RQ YDULDEOHV DUJXPHQWV DQG ILHOGV WKDW GHQRWH ZKHWKHU RU QRW REMHFWV UHDFKDEOH WKURXJK WKHP DUH UHDGRQO\ RU ZKHWKHU WKH UHIHUHQFHV DUH XQLTXH DV UHDGRQO\ GDWD LV H[HPSW IURP KDYLQJ WR EH XQLTXH 

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’îÞޜÈé VKRXOG UHIHU WR RQH HOH PHQW RI WKH OLVW ,PSOHPHQWLQJ WKLV LWHUDWLRQ ZLWK LVODQGV LV SRVVLEOH EXW QHHGV WR GHFRQVWUXFW DQG UHFRQVWUXFW WKH OLVW LQ WKH SURFHVV

%DOORRQ W\SHV E\ $OPHLGD >@ SURYLGH D W\SH DEVWUDFWLRQ WKDW KDV VLPLODU VHPDQWLFV WR LVODQGV ZLWK FHUWDLQ GLIIHUHQFHV WKH HQWU\ LQWR D VXEUHJLRQ RI WKH KHDS ZKDW LQ LVODQGV LV FDOOHG EULGJH REMHFWV  WKH EDOORRQ REMHFW FDQ QRW EH DOLDVHG IURP ILHOGV RI REMHFWV 7KHUH FDQ KRZHYHU EH WHPSRUDU\ DOLDVHV IURP VWDFN YDULDEOHV 7KH IDFW WKDW EDOORRQ REMHFWV FDQ QRW EH DOLDVHG LV OHVV H[SUHVVLYH EXW SURYLGHV D VWURQJHU JXDUDQWHH WKDQ LVODQGV WKH JXDUDQWHH WKDW WZR YDULDEOHV UHIHUULQJ WR EDOORRQ UHIHUHQFHV DUH DOZD\V GLVMRLQW ZLWK LVODQGV WKH YDULDEOHV FRXOG EH DOLDVHV 

&RPSDUHG WR LVODQGV EDOORRQV GR QRW UHTXLUH DOO UHIHUHQFHV SDVVHG LQ RU RXW RI WKHP WR EH XQLTXH 7KLV ZRUNV E\ XVLQJ LQVWHDG RI XQLTXHQHVV DW WKH ERXQGDU\ VWDWLF DQDO\VLV IRU HDFK EDOORRQ FODVV 7KLV DQDO\VLV VWHS HQVXUHV WKDW PHWKRGV RI EDOORRQ W\SHV FDQ QRW LQWURGXFH LOOHJDO VKDULQJ EHWZHHQ EDOORRQV² ZKLFK LQ WKH LVODQGV SURSRVDO LV UXOHG RXW E\ WKH XQLTXHQHVV UHTXLUHPHQW ,Q VWHDG WKH VWDWLF DQDO\VLV WUDFNV ZKLFK EDOORRQ D UHIHUHQFH LV FRPLQJ IURP DQG HQVXUHV WKDW WKH UHIHUHQFH GRHV QRW JHW SDVVHG LQWR DQRWKHU EDOORRQ 7R WUDFN WKH IORZ RI UHIHUHQFHV DFFXUDWHO\ WKH EDOORRQV V\VWHP UHTXLUHV DOO EDOORRQ UHI HUHQFHV WR EH XQLTXH &RPSDUHG WR LVODQGV EDOORRQV FDQ VWRUH D UHIHUHQFH WR DQ HOHPHQW WKDW LV LQVLGH D EDOORRQFROOHFWLRQ LQ D VWDFN YDULDEOH ZKHUH LV

(35)

ODQGV QHHG WR HODERUDWHO\ VKLIW UHIHUHQFHV RXWVLGH DQG EDFN LQVLGH D FROOHFWLRQ WR DFKLHYH WKH VDPH

%DOORRQV KDYH EHHQ VXFFHVVIXO LQ UHVHDUFK WKH\ KDYH EHHQ DSSOLHG WR SDUDO OHOLVP HJ E\ *RUGRQ HW DO >@ 6HUYHWWR HW DO >@ 

)OH[LEOH $OLDV 3URWHFWLRQ DQG 2ZQHUVKLS 7\SHV )LQH*UDLQHG (QFDSVXODWLRQ

7KH ³)OH[LEOH $OLDV 3URWHFWLRQ´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

)$3 DFKLHYHV WKH LQFUHDVHG JUDQXODULW\ WKURXJK LQYHQWLQJ DOLDVLQJ PRGHV $OLDVLQJ PRGHV DUH UHIHUHQFH DQQRWDWLRQVWKDW DQQRWDWH HDFK ILHOG RU YDULDEOH ZLWK WKH UROH WKH\ SOD\ 7KH PRVW LPSRUWDQW PRGHV DUHޜÛDQG…Þ§ D ILHOG WKDW LV DQQRWDWHG ZLWKޜÛFRQWDLQV D UHIHUHQFH WR DQ REMHFW WKDW LV SDUW RI WKH

ILHOGRZQHU¶V PXWDEOH LQQHU VLGH KHUH FDOOHG WKH ³UHSUHVHQWDWLRQ´ UHIHUHQFHV WR WKLV REMHFW FDQ QHYHU OHDN RXWVLGH WKH REMHFW WKDW KROGV WKH ILHOG²WKH LQYDUL DQW PDLQWDLQHG IRUޜÛLV VLPLODU WR LVODQGV ,Q DGGLWLRQ KRZHYHU IOH[LEOH DOLDV SURWHFWLRQ DGGV WKH…Þ§PRGH DQ REMHFW UHIHUUHG WR IURP DQ…Þ§ILHOG LV D UHIHU

HQFH WR D YDOXH VWRUHG LQVLGH D FROOHFWLRQ FDOOHG DQ ³DUJXPHQW´  7KH FROOHFWLRQ FDQ QRW PRGLI\ WKH REMHFW WKURXJK WKLV ILHOG RQO\ XVH UHDGRQO\ RSHUDWLRQV RQ WKH YDOXH

&ROOHFWLRQV FDQ EH SDUDPHWHULVHG E\ PRGHV WKH OLVW FDQ WDNH D W\SH SDUDP HWHU UHSUHVHQWLQJ WKH DOLDVLQJ PRGH RI LWV GDWD $ FOLHQW FDQ QRZ ELQG HJ LWV RZQ ޜÛWR WKH OLVW¶V DOLDVLQJ PRGH IRU WKH GDWD 7KH DELOLW\ WR SDUDPHWHULVH W\SHV LV TXLWH SRZHUIXO FRQVLGHULQJ LWV UHODWLYH VLPSOLFLW\ $ OLVW ZLWK LWHUDWLRQ LQ )$3 FRXOG EH LPSOHPHQWHG HDVLO\ LW ZRXOG EH SDUDPHWHULVHG ZLWK DQ…Þ§

PRGH WR GHFODUH WKH DFFHVV PRGH LW VKRXOG XVH WR VWRUH LWV FRQWDLQHG HOHPHQWV WKH UHVW RI LWV VWUXFWXUH WKH QRGHV  LW ZRXOG VWRUH XVLQJ WKHޜÛDFFHVV PRGH

DV WKH OLVW QHHGV IXOO ZULWH DFFHVV 7KH REMHFW ZKRVHޜÛLV ERXQG WR WKH OLVW¶V

…Þ§ WKH ³RZQHU´ RI WKH GDWD LQ WKH OLVW LV WKHQ IUHH WR LWHUDWH RYHU WKH GDWD

2ZQHUVKLS W\SHV &ODUNH 3RWWHU DQG 1REOH >@ ZHUH EXLOW RQ WKH LGHDV RI IOH[LEOH DOLDV SURWHFWLRQ 2ZQHUVKLS W\SHV SURYLGH VLPLODU DEVWUDFWLRQV EXW GLIIHU LQ PLQRU ZD\V IRU LQVWDQFH WKH\ GR QRW HQIRUFH WKDW REMHFWV PD\ RQO\



$Q REMHFW LWVHOI GRHV QRW KDYH D PRGH EXW DOO YDULDEOHV UHIHUULQJ WR WKH REMHFWV GR DQG WKH YDULDEOHV GR QRW QHFHVVDULO\ DJUHH

(36)

list current

(stack)

D ,Q RUGHU WR LWHUDWH RYHU D OLVW LQ WKH LVODQGV V\VWHP ZH

KDYH WR PRYH WKH HOHPHQWV RXW RI WKH OLVW

list current

Classes:

class List[Data] {

rep:Node[rep, Data] head; }

head

Variable declarations: rep:List[rep] list; rep:Object current;

class Node[Nodes, Data] { Nodes:Node[Nodes, Data] next; Data:Object element;

} (rep of the list)

(rep of the owner of the current stack frame) (stack)

E :KLOH D OLVW PD\ DOZD\V HQFDSVXODWH LWV QRGHV LW PD\ QRW HQFDSVXODWH LWV

GDWD IOH[LEOH DOLDV SURWHFWLRQ DQG RZQHUVKLS W\SHV GUDZQ SHUPLW WKLV XVH FDVH 6\QWD[ D W\SHÏϒϫÛϓÝϓَкϬGHQRWHV DQ REMHFW RI FODVVWKDW LV LQ WKH RZQHUVKLS FRQWH[WÏDQG ELQGV RZQHUVKLS FRQWH[WVÛÝ. . . WR LWV GRPDLQ SDUDP

HWHUV PHDQLQJ LW PD\ KROG UHIHUHQFHV LQWR WKRVH GRPDLQV

)LJXUH  ,VODQGV DUH VHPDQWLFDOO\ VLPSOH EXW WRR FRDUVHJUDLQHG IRU PDQ\ VLWXD

WLRQV )OH[LEOH DOLDV SURWHFWLRQ DQG RZQHUVKLS W\SHV DUH PRUH FRPSOH[ EXW DOVR PRUH H[SUHVVLYH

(37)

PXWDWH GDWD WKH\ RZQ GLUHFWO\ ,Q RZQHUVKLS W\SHV REMHFWV DUH JURXSHG LQ ³RZQHUVKLS FRQWH[WV´ ,Q )LJXUH E ZH FDQ VHH GLIIHUHQW RZQHUVKLS FRQWH[WV LQ XVH WKH UHSUHVHQWDWLRQ RI WKH REMHFW o RZQLQJ WKH FXUUHQW WRS VWDFN IUDPH LQ OLJKW JUH\ ZKLFK FRQWDLQV WKH OLVW WKH OLVW LWVHOI KDV LWV RZQ UHSUHVHQWDWLRQ GDUN JUH\  ZKLFK LW XVHV WR KLGH DZD\ WKH QRGHV LW FRQWDLQV ,W LV SDUDPHWHULVHG RYHU WKH OLJKW JUH\ RZQHUVKLS FRQWH[W LQ RUGHU WR PDNH WKH HOHPHQWV RI WKH OLVW± XQOLNH WKH QRGHV±DFFHVVLEOH IURP o GLUHFWO\ 2ZQHUVKLS FRQWH[WV DUH QHVWHG UHJLRQV RI WKH KHDS MXVW OLNH LVODQGV DQG EDOORRQV DUH (YHU\ FODVV LQVWDQFH LQ RZQHUVKLS W\SHV GHILQHV PDQDJHV DQ RZQHUVKLS FRQWH[W RI LWV RZQ FDOOHG ³UHS´²LWV PXWDEOH UHSUHVHQWDWLRQ OLNH LQ IOH[LEOH DOLDV SURWHFWLRQ $Q REMHFW FDQ OLNH LQ )$3 DOVR EH SDUDPHWHULVHG RYHU RZQHUVKLS FRQWH[WV 2QH GLIIHU HQFH EHWZHHQ RZQHUVKLS W\SHV DQG IOH[LEOH DOLDV SURWHFWLRQ LV WKDW WKH IRUPHU GR QRW FRQIODWH DOLDVLQJ ZLWK OLPLWDWLRQV RQ XSGDWHV PRGLILFDWLRQV WKURXJK DQ

…Þ§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…Þ§SDUDPHWHU LQ )$3±EXW…Þ§H[SUHVVHV WKLV

SURSHUW\ GLUHFWO\ ZKLOH LQ RZQHUVKLS W\SH ZLWK HIIHFWV WKLV SURSHUW\ LV OHVV GHFODUDWLYHO\ H[SUHVVHG E\ RPLVVLRQ

7KH DFFHVV PRGHV DQG RZQHUVKLS FRQWH[WV ZH KDYH FRYHUHG DUH DEVWUDFWLRQV WKDW SHUPLW DOLDVLQJ ZLWKLQ WKHP EXW DYRLG DOLDVLQJ EHWZHHQ WKHP 7KH\ JURXS WKH GDWD LQWR LGHDOO\ VPDOO EXEEOHV RI XQUHODWHG VWDWH $V WKH\ SURYLGH IRUPV RI HQFDSVXODWLRQ WKHVH V\VWHPV DUH LQKHUHQWO\ IRUPV RI GHHS DOLDV FRQWURO ± D YHU\ XVHIXO SURSHUW\ IRU UHDVRQLQJ DERXW SURJUDPV 7KH\ GR QRW UHDGLO\ OHQG WKHPVHOYHV WR H[SUHVV DEVHQFH RI DOLDVLQJ ZLWKLQ VXFK D EXEEOH OLNH H[SUHVVLQJ D OLVW ZLWK VHW VHPDQWLFV WKDW FRQWDLQV QR REMHFW WZLFH  7KH RWKHU GRPLQDQW ZD\ RI DOLDV FRQWURO WKDW ZH ZLOO FRYHU QH[W LV D GXDO RI VRUWV E\ VWDUWLQJ ZLWK UHIHUHQFHV WKDW KDYH QR DOLDVHV WKH\ HDVLO\ H[SUHVV WKH OLVW ZLWK VHW VHPDQWLFV EXW LW LV FRPSDUDEO\ KDUGHU IRU WKHVH V\VWHPV WR GHOLYHU GHHS DOLDV FRQWURO

References

Related documents

Wklv uhvxow kdv lpsruwdqw lpsolfdwlrqv1 Iluvw/ lw lv wkh hqwluh yroxph ri zruog wudgh wkdw pdwwhuv iru lqhtxdolw|dqg qrw wkh vpdoo yroxphv ri Qruwk0 Vrxwk wudgh rqo|1 Lq wklv

Lq ghyhorslqj wkh vlpxodwlrq prgho/rxu dpelwlrq kdv ehhq wr nhhs wkh prgho vlpsoh dqg wr plqlpl}h wkh qxpehu ri yduldeohv wr eh prghoohg1 Frq0 vhtxhqwo|/wkh prgho jlyhv d

Lq wklv sdshu zh frqvlghu wkh sureohp ri krz wr prgho wkh hodvwlf surshuwlhv ri zryhq frpsrvlwhv1 Pruh vshflf/ zh zloo xvh pdwkhpdwlfdo krprjh0 ql}dwlrq wkhru| dv d uhihuhqfh

Wklv uhlwhudwhg krprjhql}dwlrq frxog ri frxuvh eh jhqhudol}hg wr q vfdohv/ dqg zh frqfoxgh wkdw lw frxog eh d xvhixo wrro iru ghwhuplqdwlrq ri wkh vwlqhvv whqvruv ri shulrglf

zdv fduulhg rxw wr looxvwudwh krz wkh wzr dssurdfkhv glhu iru vrph q wrohu0 dqfh olplwv dqg vrph vdpsoh vl}hv xvlqj erwk sdudphwulf dqg qrq0sdudphwulf hvwlpdwruv1 Wkh vdpsoh

Dv fdq eh vhhq iurp Iljxuh  dqg Iljxuh 2 wkh htxdwlrq E  jlyhv d eldvhg uhvxow iru qlwh vdpsoh vl}hv1 Orrnlqj edfn dw wkh ghulydwlyhv ri htxdwlrq E  lw fdq eh vhhq wkdw

Li zh kdyh rqo| sxuh zdwhu lq wkh v|vwhp/ htxdwlrq 7155 jlyhv xv d yhu| dffxudwh hvwlpdwlrq ri wkh sursdjdwlrq wlph1 Wkhq zh dvvxph wkdw rxu vxvshqvlrq frqvlvwv ri erwk sxuh zdwhu

Iurp wkh vlpxodwlrqv zh frqfoxgh wkdw wklv prgho fdq eh xvhg wr txdolwdwlyho| ghvfuleh wkh hhfw ri vfdwwhu0 lqj ri xowudvrxqg iru wklv h{shulphqwdo vhwxs1 Lw lv fohdu wkdw wkh