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NFUBQBUIWFD4DBMBCMF 3FQSFTFOUBUJPO-FBSOJOHGPS )FUFSPHFOFPVT/FUXPSLT ,%%` :VYJBP %POH /JUFTI 7$IBXMB "OBOUISBN 4XBNJ ࿦จ঺հ!LVSJJWF

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໨࣍ wݚڀഎܠ w࿦จ֓ཁ wఏҊख๏ w࣮ݧ w݁࿦

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໨࣍ wݚڀഎܠ w࿦จ֓ཁ wఏҊख๏ w࣮ݧ w݁࿦

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ݚڀഎܠʛ)FUFSPHFOFPVT/FUXPSL<> ϊʔυɾΤοδͷλΠϓ͕ ෳ਺ଘࡏ͢ΔωοτϫʔΫ <>:J[IPV 4VOBOE+JBXFJ)BO.JOJOH)FUFSPHFOFPVT*OGPSNBUJPO/FUXPSLT1SJODJQMFTBOE.FUIPEPMPHJFT.PSHBO$MBZQPPM1VCMJTIFST

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ݚڀഎܠʛXPSEWFD<>Ԡ༻ख๏ͷڵོ • %FFQ8BML<> ϥϯμϜ΢ΥʔΫͰੜ੒ͨ͠ ϊʔυܥྻ͔Β෼ࢄදݱΛੜ੒ • -*/&<> ྡ઀͢Δϊʔυͱͷؔ܎͔Β෼ࢄදݱΛੜ੒ • OPEFWFD<> ্هख๏Λ૊Έ߹Θͤͯ෼ࢄදݱΛੜ੒ <>#SZBO1FSP[[J 3BNJ"M3GPV BOE4UFWFO4LJFOB%FFQ8BML0OMJOF-FBSOJOHPG4PDJBM3FQSFTFOUBUJPOT*O,%%`"$. r <>+JBO5BOH .FOH 2V .JOH[IF 8BOH .JOH;IBOH +VO:BO BOE2JBP[IV .FJ-*/&-BSHFTDBMF*OGPSNBUJPO/FUXPSL&NCFEEJOH*O888`"$. <>"EJUZB(SPWFSBOE+VSF-FTLPWFD/PEF7FD4DBMBCMF'FBUVSF-FBSOJOHGPS/FUXPSLT*O,%%`"$. r <> 5PNBT.JLPMPW *MZB4VUTLFWFS ,BJ$IFO (SFH4$PSSBEP BOE+F%FBO%JTUSJCVUFESFQSFTFOUBUJPOTPGXPSETBOEQISBTFTBOEUIFJSDPNQPTJUJPOBMJUZ*O/*14`r ϊʔυͷ ෼ࢄදݱΛ ֫ಘ͢Δख๏

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ݚڀഎܠʛطଘख๏ͷ՝୊ )PNPHFOFPVT/FUXPSL ʹ͸༗ޮ )FUFSPHFOFPVT/FUXPSL Ҏ߱)/ͱදه ʹ͸ෆे෼ <>:J[IPV 4VOBOE+JBXFJ)BO.JOJOH)FUFSPHFOFPVT*OGPSNBUJPO/FUXPSLT1SJODJQMFTBOE.FUIPEPMPHJFT.PSHBO$MBZQPPM1VCMJTIFST ͔͠͠

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ݚڀഎܠʛຊݚڀͷ໨త )/͕࣋ͭߏ଄ͱҙຯͷ৘ใΛ อ࣋ͨ͠෼ࢄදݱͷੜ੒

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໨࣍ wݚڀഎܠ w࿦จ֓ཁ wఏҊख๏ w࣮ݧ w݁࿦

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࿦จ֓ཁʛͲΜͳ΋ͷ͔ʁ ԿΛͨ͠ʁ )/ʹରͯ͠༗ޮͳNFUBQBUIWFDͱɺ ͦͷ೿ੜ൛NFUBQBUIWFDΛఏҊɻ ݁ՌͲ͏ͩͬͨʁ ༷ʑͳϚΠχϯάλεΫʹର͠ ࠷ઌ୺ͷख๏Λ্ճΔ͚ͩͰͳ͘ɺ ߏ଄ͱҙຯΛอ࣋ͨ͠෼ࢄදݱ͕ੜ੒Ͱ͖ͨ

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໨࣍ wݚڀഎܠ w࿦จ֓ཁ wఏҊख๏ w࣮ݧ w݁࿦

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ఏҊख๏ʛ֓ཁਤ *OQVUɿ)/(ɺNFUBQBUIεΩʔϜ1 0VUQVUɿ෼ࢄදݱߦྻ9 ࣍ݩ E ௖ ఺ ਺ 7 ͋Δ௖఺ͷ෼ࢄදݱ ผͷ௖఺ͷ෼ࢄදݱ

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ఏҊख๏ʛ)/ )FUFSPHFOFPVT/FUXPSLͷఆٛ άϥϑ(ɺ௖఺7ɺล&ɺλΠϓ5ɺ Ϛοϓؔ਺Ї W 7ˠ57 П F &ˠ5& ͷ࣌ |TV | + | TE | > 2 Λຬͨ͢άϥϑ

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ఏҊख๏ʛNFUBQBUI NFUBQBUITDIFNF JT ɿ7 ͱ7M ͷϊʔυλΠϓͷؔ܎

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ఏҊख๏ʛNFUBQBUI NFUBQBUITDIFNF

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ఏҊख๏ʛNFUBQBUI NFUBQBUIͷԿ͕خ͍͔͠ ҙຯͷ͋ΔNFUBQBUIΛઃఆ͢Ε͹ɺ ຒΊࠐΈʹ൓өͤ͞ΒΕΔ ྫʣ"1" ˠ ڞஶؔ܎ "171" ˠ ಉֶ͡ձʹ࿦จΛ ग़ͨ͠ஶऀͷؔ܎

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ఏҊख๏ʛNFUBQBUIWFD ৽نੑ͸Ͳ͜Ͱ͔͢ʁ .FUB1BUI#BTFE3BOEPN8BMLT ͰೖྗͷϊʔυܥྻΛੜ੒ ˣ )FUFSPHFOFPVT4LJQ(SBN Ͱ෼ࢄදݱΛੜ੒

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ఏҊख๏ʛ.FUB1BUI#BTFE3BOEPN8BMLT ྫ XBMLBQ"$-QBQ ,%%QB ୯७ͳϥϯμϜ΢ΥʔΫ Ͱ͸ͳ͘NFUBQBUIʹ Ԋ͍ͬͯΔ

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ఏҊख๏ʛ)FUFSPHFOFPVT4LJQ(SBN XPSEWFDͰ͸ ೖྗ୯ޠ͔Βपล୯ޠͷ༧ଌΛ ͢ΔχϡʔϥϧωοτϫʔΫͷɺ ೖྗ૚͔ΒӅΕ૚ͷॏΈ͕ೖྗ ୯ޠͷ෼ࢄදݱ *XBOUUPFBU BOBQQMFFWFSZEBZ *XBOUUPFBU BOBQQMFFWFSZEBZ

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ఏҊख๏ʛ)FUFSPHFOFPVT4LJQ(SBN NFUBQBUIWFDͰ͸ ೖྗϊʔυ͔Βपลϊʔυͷ༧ ଌΛ͢Δχϡʔϥϧωοτϫʔ Ϋͷɺೖྗ૚͔ΒӅΕ૚ͷॏΈ ͕ೖྗϊʔυͷ෼ࢄදݱ BQ"$-Q BQ,%%QB BQ"$-Q BQ,%%QB

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ఏҊख๏ʛग़ྗ X ∈ R|V|×d , d << |V| ͳΔE࣍ݩ෼ࢄදݱΛֶश ࣍ݩ E ௖ ఺ ਺ 7 ͋Δ௖఺ͷ෼ࢄදݱ ผͷ௖఺ͷ෼ࢄදݱ

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ఏҊख๏ʛNFUBQBUIWFD ͸Կʁ /FHBUJWF4BNQMJOH Λ֦ு

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ఏҊख๏ʛNFUBQBUIWFD /FHBUJWF4BNQMJOHʢҎલͷख๏ʣ ˠपล୯ޠͷ֬཰͕ʹɺपลʹ͸ͳ͍୯ޠͷ֬཰͕ ʹۙͮ͘Α͏ʹχϡʔϥϧωοτϫʔΫͷॏΈΛֶश BQ"$-Q BQ,%%QB )FUFSPHFOFPVT/FHBUJWF4BNQMJOHʢʣ ˠϊʔυͷλΠϓ͝ͱʹ/FHBUJWF4BNQMJOH BQ"$-Q BQ,%%QB

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໨࣍ wݚڀഎܠ w࿦จ֓ཁ wఏҊख๏ w࣮ݧ w݁࿦

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࣮ݧʛ࣮ݧ֓ཁ ̏ͭͷ࣮ݧʹΑΓఏҊख๏ͷ༗ޮੑΛௐࠪ • ଟΫϥε෼ྨ • ΫϥελϦϯά • ྨࣅ౓ݕࡧ Ճ͑ͯɺՄࢹԽͱεέʔϥϏϦςΟΛௐࠪ

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࣮ݧʛσʔληοτ • ".JOFS $PNQVUFS4DJFODF<> ສҎ্ͷݚڀऀɺສҎ্ͷ࿦จɺ ۙ͘ͷֶձ • %BUBCBTFBOE*OGPSNBUJPO4ZTUFNT<> ۙ͘ͷֶձɺͦ͜ʹ͓͚Δͷ τοϓஶऀɺສҎ্ͷ࿦จ <> +JF 5BOH +JOH;IBOH -JNJO :BP +VBO[J -J -J;IBOH BOE;IPOH 4V"S OFU.JOFS&YUSBDUJPOBOE.JOJOHPG"DBEFNJD4PDJBM/FUXPSLT*O,%%`r <> :J[IPV 4VO +JBXFJ)BO 9JGFOH :BO 1IJMJQ4:V BOE5JBOZJ 8V1BUITJN.FUBQBUICBTFEUPQLTJNJMBSJUZTFBSDIJOIFUFSPHFOFPVTJOGPSNBUJPOOFUXPSLT*O 7-%#`r

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࣮ݧʛ࣮ݧઃఆ • ϊʔυ͋ͨΓͷࢼߦճ਺ɿ • ࢼߦ͋ͨΓͷา਺ɿ • ϕΫτϧͷ࣍ݩ਺ɿ • ۙྡαΠζɿ • ωΨςΟϒαϯϓϧ਺ɿ

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࣮ݧʛൺֱख๏ • %FFQ8BML<>OPEFWFD<> ύϥϝʔλʔΛௐ੔ͯ͠ಉҰख๏ͱͯ͠ѻ͏ • -*/&<> ྡ઀͢Δϊʔυͱͷؔ܎͔Β෼ࢄදݱΛੜ੒ • 15&<> ୯ޠɾจॻɾϥϕϧͷؔ܎Λάϥϑʹද͠ɺ ͦͷάϥϑ͔ΒϕΫτϧදݱΛֶश

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࣮ݧʛଟΫϥε෼ྨʢਫ਼౓ʣ ʙͷ޲্ ʙͷ޲্

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࣮ݧʛଟΫϥε෼ྨʢύϥϝʔλʔʣ ɾBVUIPSDMVTUFSJOH ਫ XͱMͱE͸େ͖͘ͳΔʹͭΕਫ਼౓΋޲্ L͕େ͖͘ͳΔʹͭΕਫ਼౓͸ѱԽɺ ͜Ε͸IPNPHFOFPVTFOWJSPONFOU<> Ͱͷ݁Ռͱਅٯ ɾWFOVFDMVTUFSJOH ੨ ͋·Γਫ਼౓ʹӨڹ͠ͳ͍

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࣮ݧʛϊʔυΫϥελϦϯάʢਫ਼౓ʣ 15&ΑΓˋ޲্ 15&ΑΓˋ޲্

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࣮ݧʛϊʔυΫϥελϦϯάʢύϥϝʔλʔʣ ɾBVUIPSDMVTUFSJOH ੨ XͱM͸େ͖͘ͳΔʹͭΕਫ਼౓΋޲্ EͱL͸େ͖͘ͳΔʹͭΕਫ਼౓͸ѱԽ ɾWFOVFDMVTUFSJOH ੺ L͸େ͖͘ͳΔʹͭΕҰ౓ਫ਼౓͕޲্͠ɺͦͷޙѱԽ͢Δ

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࣮ݧʛྨࣅݕࡧ ଟ͘ͷ෼໺ʹ͓͍ͯɺ ݕࡧΫΤϦͱಉ͡෼໺ͷτοϓֶձ͕ τοϓͷதʹೖ͍ͬͯΔ

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࣮ݧʛՄࢹԽ ఏҊख๏Ͱ͸XPSEWFDʹ͓͚Δ ࠃͱट౎ͷରԠؔ܎ͷΑ͏ʹɺ ֶձͱͦͷ෼໺ͷஶ໊ͳݚڀऀͷ ରԠؔ܎ֶ͕शͰ͖͍ͯΔ

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࣮ݧʛՄࢹԽ ࣍ݩʹ౤Ө͢Δͱ ͍ۙ෼໺ͷֶձ͕ۙ͘ʹଘࡏ

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࣮ݧʛεέʔϥϏϦςΟ ཧ૝తͳઢܗͰ͸ͳ͍͕ ४ઢܗͷύϑΥʔϚϯε

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໨࣍ wݚڀഎܠ w࿦จ֓ཁ wఏҊख๏ w࣮ݧ w݁࿦

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݁࿦ʛ'VUVSF8PSL NFUBQBUIੜ੒࣌ͷܭࢉྔ࡟ݮ NFUBQBUIͷࣗಈֶश ωοτϫʔΫͷਐԽ΁ͷରԠ ϞσϧͷҰൠԽ

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݁࿦ʛ·ͱΊ ԿΛͨ͠ʁ )/ʹରͯ͠༗ޮͳNFUBQBUIWFDͱɺ ͦͷ೿ੜ൛NFUBQBUIWFDΛఏҊɻ ݁ՌͲ͏ͩͬͨʁ ༷ʑͳϚΠχϯάλεΫʹର͠ ࠷ઌ୺ͷख๏Λ্ճΔ͚ͩͰͳ͘ɺ ߏ଄ͱҙຯΛอ࣋ͨ͠෼ࢄදݱ͕ੜ੒Ͱ͖ͨ