4XHU\%DVHG 6QDSVKRW $QDO\VLV
7KH ³)R[´ WRRO E\ 3RWDQLQ 1REOH DQG %LGGOH >@ DQDO\VHV VQDSVKRWV RI SUR JUDPV WR VHDUFK IRU DPRQJVW RWKHU SURSHUWLHV REMHFW XQLTXHQHVV DQG HYLGHQFH RI QHVWHG KHDS VWUXFWXUHV VLPLODU WR WKH RQHV WKDW RZQHUVKLS W\SHV HQIRUFH 7KH\ GHILQH RZQHUVKLS DV JUDSKGRPLQDWLRQ %XW WKDW GHILQLWLRQ WKH\ QRWH LV SR WHQWLDOO\ QRW \LHOGLQJ WKH UHVXOW WKDW RQH ZRXOG H[SHFW WKH DXWKRUV QRWH WKDW WKH ³DYHUDJHGHSWK´ PHWULF WKDW PHDVXUHV WKH DYHUDJH GHSWK RI DOO REMHFWV LQ WKH RZQHUVKLS WUHH YDULHV JUHDWO\ EHWZHHQ DSSOLFDWLRQV :KHQ LQYHVWLJDWLQJ WKLV FLUFXPVWDQFH WKH\ IRXQG WKDW WKHLU GHILQLWLRQ KDG FODVVLILHG PDQ\ RI OLQNHG GDWD VWUXFWXUHV DV GHHS RZQHUVKLS KLHUDUFKLHV WR JLYH DQ H[DPSOH MXVW ORRNLQJ DW JUDSK GRPLQDWLRQ D VLQJO\ OLQNHG OLVW ZRXOG EH VHHQ DV KDYLQJ WKH RZQHUVKLS VWUXFWXUH LQ )LJXUH 7KH SURJUDPPHU¶V PHQWDO YLHZ RI RZQHUVKLS LQ WKLV FDVH WKRXJK LV PRVW OLNHO\ WKDW WKH KHDG RI WKH OLVW RZQV DOO WKH QRGHV ZKLFK DUH DW D VLQJOH OHYHO
1 7 2 9 13 4 8
)LJXUH 8VLQJ WKH GRPLQDWRU UHODWLRQ WR PLQH IRU RZQHUVKLS JLYHV XV RYHUO\ GHHSO\
QHVWHG UHVXOWV 7KH SURJUDPPHU¶V PHQWDO PRGHO RI WKH GDWD VWUXFWXUH ZDV PRVW OLNHO\ WR RQO\ GUDZ WKH RXWHUPRVW RZQHUVKLS FRQWH[W
$ QRGHn LQ D JUDSK GRPLQDWHV DQRWKHU QRGH nLI DOO SDWKV WRnSDVV WKURXJKn WKLV LV VLPLODU
WR RXU GHILQLWLRQ RI HQFDSVXODWLRQ 'HILQLWLRQ S
7KH\ PLWLJDWH WKLV SUREOHP E\ FRXQWLQJ VXFFHVVLYH FKDLQV RI REMHFWV RI WKH VDPH W\SH WR FRXQW DV FKDLQV RI OHQJWK WKHUHE\ SXWWLQJ DOO QRGHV RI WKH OLVW DW WKH VDPH GHSWK
)R[ FRPHV ZLWK D TXHU\ ODQJXDJH WKDW OHWV XVHUV IRUPXODWH WKHLU RZQ TXHULHV ZH ZLOO TXRWH VRPH RI WKH UHVXOWV REWDLQHG LQ 6HFWLRQ
4XHU\%DVHG 7UDFH $QDO\VLV
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
&KDSWHU 3DSHU ,, DQG 3DSHU ,,, WUHDW WKLV FRQWULEXWLRQ LQ PRUH GHWDLO
6XPPDULHV RI 6QDSVKRWV
:RUN E\ 0LWFKHOO >@ DWWHPSWV WR VXPPDULVH ODUJH VQDSVKRWV RI SURJUDP KHDSV LQ RUGHU WR PDNH WKH SURJUDP PRUH HDV\ WR XQGHUVWDQG E\ GHYHORSHUV 7R VXP PDULVH PHDQV WR VLPSOLI\ WKH SURJUDP¶V PHPRU\ JUDSK E\ FOXVWHULQJ FRQQHFWHG REMHFWV LQWR UHSUHVHQWDWLYH QRGHV 7KH UHVXOWLQJ JUDSK LGHDOO\ KLGHV LUUHOHYDQW GHWDLO EXW SUHVHUYHV WKH HVVHQWLDO ELUGVH\H YLHZ RI D SURJUDP¶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³UHSUHVHQWDWLYH REMHFW´ DQG FKDQJLQJ HGJHV WR RULJLQDWHUHIHU WR WKH UHVSHFWLYH UHSUHVHQWDWLYH REMHFW 7KHVH JUDSK HGLWV UHFRJQLVH D YDULHW\ RI FRPPRQ VWUXFWXUHV WKDW DSSHDU LQ SURJUDPV DQG SLFNV IRU D JURXS RI REMHFWV D UHSUHVHQWDWLYH REMHFW WKDW LW NHHSV LQ WKH JUDSK LQVWHDG RI WKH JURXS )RU H[DPSOH REMHFWV WKDW DUH GRPLQDWHG E\ DQRWKHU DUH UHPRYHG IURP WKH JUDSK DQG WKH GRPLQDWRU LV NHSW DV WKHLU UHSUHVHQWDWLYH 7KH DOJRULWKP SURGXFHV RYHUYLHZV RI SURJUDP PHPRU\ WKDW FRQWDLQ RQO\ D VPDOO
VHW RI UHPDLQLQJ QRGHV PXFK OHVV WKDQ LQ WKHLU H[DPSOHV RI UHDOZRUOG SURJUDPV ZLWK FRPSXWDWLRQ WLPHV WKDW DUH LQ WKH VHFRQGV WR PLQXWHV UDQJH
6WDWLF $QDO\VLV DQG 7\SH ,QIHUHQFH
+DFNHWW DQG $LNHQ >@ EXLOG D VWDWLF DQDO\VLV RI DOLDVLQJ ZKLFK WKH\ XVH WR DQDO\VH PRUH WKDQ RQH PLOOLRQ OLQHV RI & FRGH ,Q DGGLWLRQ WR LPSOHPHQWLQJ D VFDODEOH VWDWLF DQDO\VLV WKHLU FRQWULEXWLRQ LV PDQXDOO\ FODVVLI\ DOO RFFXUUHQFHV RI DOLDVLQJ ILQGLQJ WKDW ³MXVW QLQH LGLRPV RI DOLDVLQJ DFFRXQW IRU QHDUO\ DOO DOLDVLQJ LQ >WKH@ VWXG\´ 6XFK D ILQGLQJ LV LPSRUWDQW LW VXJJHVWV WKDW ODQJXDJH FRQVWUXFWV FDQ EH EXLOW FRPSDUDEO\ HDVLO\ WKDW FDQ H[SUHVV DOLDVLQJ DW D KLJKHU OHYHO RI DEVWUDFWLRQ WKDQ VLPSO\ XVLQJ UHIHUHQFHV IRU DOO DSSOLFDWLRQV RI DOLDVLQJ :H ZLOO GHVFULEH WKHLU UHVXOWV LQ FORVHU GHWDLO LQ 6HFWLRQ
:RUN E\ 4XLQRQH] 7VFKDQW] DQG (UQVW >@ LQWURGXFHV WKH -DYDULILHU WRRO WKDW VWDWLFDOO\ DQDO\VHV -DYD VRXUFH FRGH DQG DQQRWDWHV LW WR XVH WKH UHIHUHQFH LP PXWDELOLW\ RI WKH SUHYLRXVO\ H[LVWLQJ -DYDUL -DYD GLDOHFW WKDW ZH KDYH SUHVHQWHG LQ 6HFWLRQ 7KH V\VWHP LQIHUV W\SH DQQRWDWLRQV E\ HPLWWLQJ FRQVWUDLQWV E\ GHIDXOW D YDULDEOH LV UHDGRQO\ 7\SH FRQVWUDLQWV DUH XVHG WR UHFRUG GHYLDWLRQV IURP WKLV GHIDXOW WKH W\SH FRQVWUDLQWÿVWDWHV WKDW YDULDEOHÿLV PXWDEOH 7KLV FRQVWUDLQW ZRXOG EH JHQHUDWHG IURP DQDO\VLQJ D VWDWHPHQW OLNHÿϘ¦ Ѻ Ā 7KHUH DUH DOVR JXDUGHG FRQVWUDLQWV WKDW DUH JHQHUDWHG E\ DQDO\VLQJ GHUHIHUHQFHV RI ILHOGV DQG DVVLJQPHQWV )RU LQVWDQFH WKH VWDWHPHQWÿ Ѻ ĀZRXOG JHQHUDWH WKH FRQVWUDLQWÿϿѼĀ PHDQLQJ WKDWÿEHLQJ D PXWDEOH YDULDEOH LPSOLHV WKDWĀPXVW DOVR EH PXWDEOH 6LPLODUO\ D PHWKRG FDOOĀϘÇϭÛَкϮJHQHUDWHV DPRQJVW RWKHU FRQVWUDLQWV D JXDUGHG FRQVWUDLQW WKDW VWDWHV WKDW LI WKH 鬯âUHIHUHQFH LQVLGH WKHÇPHWKRG LV PXWDEOH VR PXVW EHĀ 6ROYLQJ WKHVH FRQVWUDLQWV ZRUNV E\ HV VHQWLDOO\ XVLQJ XQJXDUGHG FRQVWUDLQWVÿWR WULJJHU JXDUGHG FRQVWUDLQWVÿϿѼĀDQG DGGLQJĀWR WKH FRQVWUDLQW SRRO H[HFXWLQJ WKLV SURFHVV XQWLO QR IXUWKHU JXDUGHG FRQVWUDLQWV FDQ EH PDWFKHG
7KH 5H,P W\SH V\VWHP DQG 5H,P,QIHU WRRO E\ +XDQJ HW DO >@ VLPLODUO\ WR -DYDULILHU LQIHUV UHIHUHQFH LPPXWDELOLW\ W\SH DQQRWDWLRQV LQ DQ H[WHQGHG YHU VLRQ RI -DYD :RUN E\ 0LODQRYD DQG 'RQJ >@ H[WHQGV 5H,P E\ +XDQJ HW DO >@ E\ HOHJDQWO\ FRQVWUXFWLQJ VXSSRUW IRU GHHS REMHFW LPPXWDELOLW\ RQ WRS RI VXSSRUW IRU UHIHUHQFH LPPPXWDELOLW\ DV ZH KDYH PHQWLRQHG LQ 6HFWLRQ WKH FRUH LGHD LV WR VSOLW DQ REMHFW¶V OLIH WLPH LQWR WZR SKDVHV RQH SKDVH ZKHUH WKH REMHFW LV LQLWLDOLVHG DQG RQH SKDVH ZKHUH LW LV XVHG ZLWKRXW IXUWKHU PXWD WLRQ ,I WKH V\VWHP FDQ VKRZ WKDW DW WKH HQG RI WKH LQLWLDOLVDWLRQ SKDVH WKH IRO ORZLQJ SURSHUWLHV KROG LW FDQ VRXQGO\ FRQFOXGH WKDW WKH REMHFW LWVHOI LV REMHFW LPPXWDEOH
± 7KHUH LV RQO\ RQH FDQRQLFDO UHIHUHQFH WR WKH REMHFW
± 7KH REMHFW RQO\ FRQWDLQV UHIHUHQFHV WR RWKHU LPPXWDEOH REMHFWV ± 7KH FDQRQLFDO UHIHUHQFH LV IURP KHUH RQ UHIHUHQFH LPPXWDEOH
:RUN E\ +DOOHU DQG $[HOVVRQ > @ FRQWULEXWHV D 6FDOD FRPSLOHU SOXJLQ WKDW FRQGXFWV D VWDWLF DQDO\VLV RI 6FDOD SURJUDPV LQ RUGHU WR HPSLULFDOO\ VWXG\ KRZ
FRPPRQ VKDOORZ DQG GHHS FODVV LPPXWDELOLW\ LQ 6FDOD SURJUDPV LV 7KH\ DOVR FDWHJRULVH W\SHV WKDW DUH QRW LPPXWDEOH E\ UHDVRQV IRU ZK\ WKH\ DUH
+RZ &RPPRQ 8QLTXHQHVV (QFDSVXODWLRQ DQG
,PPXWDELOLW\ DUH LQ 3UDFWLFH
7KH NLQG RI UHVXOWV WKDW WKH V\VWHPV LQ 6HFWLRQ SURGXFH DUH H[WUHPHO\ YDULHG DQG HYHQ WKH SXUSRVHV WKH\ ZHUH EXLOW IRU DUH 7KLV VRPHWLPHV PDNHV LW GLIILFXOW WR FRPSDUH WKH UHVXOWV REWDLQHG IURP WKHVH ZRUNV HVSHFLDOO\ ZKHQ PLQLQJ IRU HQFDSVXODWLRQ
,W LV VWLOO SRVVLEOH WR VXPPDULVH WKH UHVXOWV WKDW WKH\ REWDLQ WKDW DUH UHOHYDQW WR WKLV WKHVLV :H ZLOO VXPPDULVH WKH PRVW UHOHYDQW UHVXOWV SUHIHUULQJ WR JLYH QXPEHUV IRU WKH VWURQJHVW SURSHUWLHV WKDW WKH UHVHDUFK LQYHVWLJDWHV
,PPXWDELOLW\
,PPXWDELOLW\ KDV EHHQ LQYHVWLJDWHG E\ D FRPSDUDEO\ ODUJH QXPEHU RI SURSRVDOV 7DEOH FRQWDLQV DQ RYHUYLHZ RI WKH V\VWHPV ZKRVH UHVXOWV ZH PHQWLRQ KHUH DQG ZKDW NLQG RI UHVXOWV WKRVH V\VWHP GHOLYHU DQG ZKDW WHFKQLTXH WKH\ XVH
+DOOHU DQG $[HOVVRQ > @ UHSRUW WKDW RI WKH 6FDOD SURJUDPV WKH\ DQDO\VH EHWZHHQ DQG RI WKH W\SHV WKH\ DQDO\VH DUH GHHSO\ SHUPDQHQWO\ FODVV LPPXWDEOH RU ³FRQGLWLRQDOO\ LPPXWDEOH´ $ FRQGLWLRQDOO\ LPPXWDEOH W\SH LV RQH WKDW LV FRQYHQWLRQDOO\ GHHSO\ LPPXWDEOH EXW KDV HJ D W\SH SDUDPHWHU WKDW PD\ EH ERXQG WR W\SH ZLWK XQNQRZQ LP PXWDELOLW\
4XLQRQH] 7VFKDQW] DQG (UQVW >@ ILQG WKDW EHWZHHQ ± RI DOO UHI HUHQFH W\SH YDULDEOHV DQG ILHOGV FDQ EH DQQRWDWHG DV GHHSO\ UHDGRQO\
6SHQFHU LQ 3DSHU ,,, VKRZV WKDW RQ DYHUDJH RI DOO REMHFWV LQ -DYD SURJUDPV DUH SHUPDQHQWO\ GHHSO\ REMHFW LPPXWDEOH DQG RI WKH FODVVHV WKDW SURGXFH DW OHDVW LQVWDQFHV SURGXFH RQO\ LPPXWDEOH REMHFWV WKHVH W\SHV PLJKW KDYH GHHS FODVV LPPXWDELOLW\ 6SHQFHU LV DQ XQVRXQG G\QDPLF DQDO\
7DEOH 7KH DQDO\VLV WRROV UHIHUUHG LQ 6HFWLRQ DQG WKH JUDQXODULWLHV WKH\ DQDO \VH /HJHQG d) DQDO\VHV GHHS LPPXWDELOLW\ s) DQDO\VHV VKDOORZ LPPXWDELOLW\ d + s) DQDO\VHV ERWK GHHS DQG VKDOORZ LPPXWDELOLW\
7RRO↓ *UDQXODULW\ → 5HI 2EM &ODVV ,PP
7HFKQLTXH
+DOOHU DQG $[HOVVRQ > @ d+s 6WDWLF DQDO\VLV +DFNHWW DQG $LNHQ >@ s s s 6WDWLF DQDO\VLV 4XLQRQH] 7VFKDQW] DQG
(UQVW >@
d 7\SH LQIHUHQFH 0LODQRYD DQG 'RQJ >@ d d 7\SH LQIHUHQFH 3DSHU ,, 3DSHU ,,, d+s d+s 7UDFH DQDO\VLV
VLV LW PLJKW MXGJH WKDW DQ REMHFW LV LPPXWDEOH RQO\ EHFDXVH LW ZDV QRW PXWDWHG IRU D SDUWLFXODU H[HFXWLRQ HYHQ WKRXJK LW ZRXOG KDYH EHHQ ZLWK RWKHU H[HFX WLRQV ZH FDQ FRQWUDVW WKDW E\ D VRXQG DQDO\VLV E\ 0LODQRYD DQG 'RQJ >@ WKDW ILQGV WKDW RI DOO REMHFWV DUH SHUPDQHQWO\ GHHSO\ REMHFW LPPXWDEOH RU WHPSRUDULO\ GHHSO\ LPPXWDEOH WKHLU DQDO\VLV DOVR ILQGV ODWH LQLWLDOLVDWLRQV RI GHHSO\ LPPXWDEOH REMHFWV
6XPPDU\
(YHQ WKRXJK WKH SUHVHQWHG WHFKQLTXHV YDU\ D ORW WKH DPRXQW RI LPPXWDELOLW\ LQ -DYD SURJUDPV LV KLJK 6FDOD SURJUDPV KDYH HYHQ KLJKHU QXPEHUV 7KLV PLJKW EH H[SODLQHG E\ 6FDOD EHLQJ VWURQJO\ LQIOXHQFHG E\ IXQFWLRQDO SURJUDPPLQJ
/RRNLQJ DW WKH GDWD UHSRUWHG E\ DOO WKHVH V\VWHPV LW VHHPV WR XV WKDW VXSSRUW IRU GHHS LPPXWDELOLW\ LQ SURJUDPPLQJ ODQJXDJHV LV DQ DGGLWLRQ WKDW OHWV SUR JUDPPHUV PRUH UHOLDEO\ LPSOHPHQW WKH IRUPV RI LPPXWDELOLW\ WKDW WKH\ DOUHDG\ KHDYLO\ XVH LQ WKHLU SURJUDPV