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1SPCMFNTFUUJOH 'JMUFSJOH!L w /PSNBMMZ XIBUVTFSTXBOUUPTFBSDIJT 4&31XJUINBYJNJ[FESFMFWBODF w 8FCTFBSDI 4/4 TUSFBNJOHTFSWJDF &$ FUD w .BOZTFSWJDFTTVQQPSUTPSUJOHCZ BUUSJCVUFT UJNF QSJDF FUD w 'PSFYBNQMF UIF4&31PGlJQIPOFzPO "NB[POJOUIFPSEFSPGUIFMPXFTUQSJDF w *UFNTXJUIMPXSFMFWBODFXJMMCFPO UPQ XIJDIXJMMMFBEQPPS69 4&31PGlJQIPOFzJOUIFPSEFSPGUIFMPXFTUQSJDF
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1SPCMFNTFUUJOH 'JMUFSJOH!L w 5IFMJTUPGSFMFWBODF JTHJWFO w 0SEFSJTTQFDJpFE w 3FUVSOVQUPLTVCMJTUUIBUNBYJNJ[FNFUSJD2 w .FUSJD2JT GPSFYBNQMF %$( R = [r1 , . . . , rn ]

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.FUIPETCZ/BÏWF)FVSJTUJDT w $VUP⒎015<> w 'JMUFSXJUIQSFEFUFSNJOFESFMFWBODFUISFTIPME w 5IFO pMUFSJUXJUI015 PQUJNBMpMUFSJOH w *OUIFXPSTUDBTF UIFSFJTOPHVBSBOUFFPGBQQSPYJNBUJPOFSSPS BDDVSBDZ w #FDBVTFJUEFQFOETPOUIFUISFTIPMETFUUJOH w 5JNFDPNQMFYJUZEPFTOPUJNQSPWF w *OUIFXPSTUDBTF ZFU w 5PQL015<> w $BMDVSBUFGPSBMJTUPGUPQL w 5IFO pMUFSJUXJUI015 PQUJNBMpMUFSJOH w 5IFNFUSJDNBZCFNBYJNJ[FECZNBLJOHUIFMJTUMFTTUIBOL w $BOQSPWFPQUJNBM BQQSPYJNBUFFSSPSJT w *OUIFXPSTUDBTF UIFUJNFDPNQMFYJUZJT Θ(nk) Θ(n log k + k2) [14] Spirin+ 2015. Relevance-aware Filtering of Tuples Sorted by an Attribute Value via Direct Optimization of Search Quality Metrics

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Џ'JMUFSJOH w )FVSJTUJDTBT$VUP⒎015BOE5PQL015DBOOPUDPOUSPMUIFBQQSPYJNBUF FSSPS w Џ'JMUFSJOHpOETBOBQQSPYJNBUFTPMVUJPOXJUIBHVBSBOUFFEFSSPSMFTTUIBO HJWFOFSSPSЏ w 5JNFDPNQMFYJUZJT w Џ'JMUFSJOHJTTUFQTBTGPMMPXT w 3JHIU1SVOJOH w %JTDSFUJ[BUJPO w 5ISFTIPMEJOH 0 < ϵ < 1 Θ(n + k2 log(1−ϵ) (ϵ/k))

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3JHIU1SVOJOH w &YBNQMF w 0SJHJOBMMJTUJT BOE w %SPQ BOEMFBWFPOMZ w *OEFFE UIFMBSHFTU%$(TPMVUJPOJT w 5IFFMFNFOUMFGUCZ3JHIU1SVOJOHJTDBMMFESJHIULNBYJNBM w 5IFPQUJNBMTPMVUJPODPOTJTUTPOMZPGSJHIULNBYJNBM FMFNFOUT -FNNB R = [0.9,1.0,1.0,1.0] k = 3 0.9 [1.0,1.0,1.0] [1.0,1.0,1.0]

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3JHIU1SVOJOH"MHPSJUIN w 6TFBQSJPSJUZRVFVFBT BOBVYJMJBSZEBUBTUSVDUVSF w 4DBOBSSBZGSPNCBDL w *GUIFFMFNFOUTSFMFWBODF JTHSFBUFSUIBOUIFMPXFTU SFMFWBODFJOUIFQSJPSJUZ RVFVF 
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5IF8PSTU$BTFPG
 3JHIU1SVOJOH w 8IFOUIFMJTUJTTVDIUIBUUIFSFMFWBODFJTHSBEVBMMZ SFEVDFE JUDBOOPUCFpMUFSFEBUBMM w &Y BOE w "MMFMFNFOUTPG3BSFSJHIUNBYJNBM w *NQSPWFUIFTFDBTFTXJUIUIFOFYUTUFQPG %JTDSFUJ[BUJPO R = [1.2,1.1,1.0,0.9] k = 3

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%JTDSFUJ[BUJPO w &Y FMFNFOUTJO3 w 8IFOUIF%JTDSFUJ[BUJPOTUFQJTBQQMJFE UIFGPMMPXJOHJOUFSWBMTBSFDSFBUFE w w w ʜ w w w %JTDSFUJ[FEMJTU JT w 4P %JTDSFUJ[BUJPOJOUIJTXBZDBVTFTFMFNFOUTUPCFpMUFSFECZ3JHIUQSVOJOH R = [3.00,2.99,2.98,...,0.01] [0.01,0.019) [0.019,0.039) [1.45,2.17) [2.17,3.0) Rϵ [2.17,...,2.17,1.45,...,1.45,...,0.01]

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5IF8PSTU$BTFPG %JTDSFUJ[BUJPO w 'JYJOH BOENBLJOH MBSHFFOPVHITPUIBUN OVNCFSPGJOUFSWBMT JTFRVBMUPO MFOHUIPGMJTU w &Y w "UUIJTUJNF BMMFMFNFOUTBSFTFMFDUFEFWFOJG %JTDSFUJ[BUJPO3JHIU1SVOJOH rmin rmax R = [100000000,10000,1]

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5ISFTIPMEJOH w 'JMUFSFMFNFOUTCFMPXUISFTIPME w #ZpMUFSJOHFMFNFOUTCFMPXUIFUISFTIPME UIFWBMVFPG DBOCFJODSFBTFE BOEBTBSFTVMU OVNCFSPGJOUFSWBMTNDBOCFEFDSFBTFE w ˠ3JHIU1SVOJOHXPSLTXFMM w FMFNFOUT w %$(PG3JT w 'JMUFSBMMFMFNFOUT %$(JTBSPVOE w "DIJFWFTBQQSPYJNBUJPO w "OEGBTUFSRVFSZQSPDFTTJOH t = g−1(ϵg(rmax /k)) rmin R = [5,0.1,...,0.1]

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