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情報特別演習最終発表
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Junya
January 10, 2022
Research
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情報特別演習最終発表
学部2年次に履修した情報特別演習の成果報告.
Junya
January 10, 2022
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Transcript
Ԭ෦७ ใಛผԋश࠷ऴൃද ߤۭωοτϫʔΫͷϋϒஔ࠷దԽ
w ۭߓͱۭߓͷؒʹ࿏ઢ͕ෑ͔Εͯ ͍Δ w ۭߓΛϊʔυɼ࿏ઢΛΤοδͱ͠ ͨͱ͖ʹߤۭ͕༗άϥϑʹͳͬ ͍ͯΔ ߤۭωοτϫʔΫͱ ʢྫʣ1FBDI"WJBUJPOͷߤۭωοτϫʔΫ 1FBDI"WJBUJPOެࣜ)1ΑΓҾ༻
w बߤ࿏ઢ͕ଟ͘ɺҠಈͷڌͱͳ ΔۭߓΛϋϒۭߓͱ͍͏ w ຊࠃͰӋాۭߓҏ୮ۭߓɼ৽ઍ ࡀۭߓͳͲ ϋϒۭߓͱ ʢྫʣ1FBDI"WJBUJPOͷߤۭωοτϫʔΫ 1FBDI"WJBUJPOެࣜ)1ΑΓҾ༻
ϋϒஔ࠷దԽͱ ֓ཁ w ͍͔ͭ͘ͷۭߓ͕༩͑ΒΕɺҙͷۭߓؒͷधཁͱ༌ૹίετ͕Θ͔ͬ ͍ͯΔ w ͦͷத͔Β͍͔ͭ͘ͷϋϒۭߓΛઃஔ͠ɺ͏·͘࿏ઢΛෑ͘͜ͱͰωοτϫ ʔΫશମͷ૯༌ૹίετΛ࠷খԽ͢Δ w ࠷খʹͳΔΑ͏ͳϋϒͷΈ߹Θͤɼ࿏ઢͷෑ͖ํΛٻΊΔ
ϋϒஔ࠷దԽͱ ຊԋशͷత w աڈͷϋϒஔͷݚڀͷྲྀΕΛѲ͢Δ w ʙʹେ͖͘ൃలͨ͠ w ϋϒஔϞσϧΛఏҊ͠ɼ࣮ࡍʹ࠷దԽΛߦ͏ ࠷దԽͷΠϝʔδਤ
γϯΫग़൛)1ΑΓൈਮ
ϋϒஔ࠷దԽͱ มͷఆٛ w ݸͷۭߓ w ߤۭωοτϫʔΫΛάϥϑ Ͱද͢ w ۭߓ
͔Βۭߓ ʢ ʣͷधཁΛ ίετΛ Ͱද͢ w ϋϒؒͷׂҾҼࢠΛ w εέʔϦϯάϑΝΫλʔͱݺΕΔ N V = {v1 , v2 , …vN } G = (V, E) vi vj vi , vj ∈ V hij Cij α (0 ≤ α ≤ 1)
ϋϒஔ࠷దԽͱ มͷఆٛ w ۭߓ ͕ϋϒۭߓͰ͋Δ͔Λද͢ม ʢϋϒͰ͋Εɼඇϋϒʣ w ۭߓ ͕ۭߓ ʹଓ͢Δ͔Λද͢ม
ʢଓ͢ΔͳΒɼ͠ͳ͍ͳΒʣ vi Xi i j Yij తؔΛ࠷খʹ͢Δ ΛٻΊΔ Xi , Yij
ϋϒஔ࠷దԽͱ ͠͞ w ݸͷۭߓ͔Β ݸͷϋϒۭߓΛબ ௨Γ w ݸͷϋϒͰͳ͍ۭߓ͕୯Ұͷϋϒۭߓʹଓ͢Δͱ͖ͷଓͷ߹ͤ ௨Γ N
p N Cp N − p pN−p શ୳ࡧͰٻղෆՄೳ
ۭߓʹରͯ͠ ߹͕ͤࢦؔతʹ૿͑ΔͨΊશྻڍ͕ࠔ ʢ͍͔ͭ͘ͷԾఆΛͨ͠ʣ ϞσϧΛߏஙͯ͠࠷దղΛಋ͘
Ϟσϧͷհ w 4JOHMF"MMPDBUJPO.PEFM w ࠷୯७ͳϞσϧ w 1)VC.FEJBO-PDBUJPO.PEFM 1.- w
͞·͟·ͳϞσϧͷͱʹͳ͍ͬͯΔϞσϧ w ఏҊ͢ΔϞσϧ w 1.-Λͱʹ֦ு
4JOHMF"MMPDBUJPO.PEFM ֓ཁ w ϋϒͰͳ͍ϊʔυ୯ҰͷϋϒʹͷΈଓՄೳ w ϋϒͰͳ͍ϊʔυಉ࢜ଓ͠ͳ͍ w ௨ΓͷϋϒͷΈ߹ΘͤΛࢼͤྑ͍ w w
w N 4JOHMF)VC-PDBUJPO.PEFMͷΠϝʔδ ʢࣈҠಈίετʣ
4JOHMF"MMPDBUJPO.PEFM ײతͳΠϝʔδ † ᶃ ᶄ ᶅ ϊʔυΛϋϒʹ͢Δ ϊʔυΛϋϒʹ͢Δ ϊʔυΛϋϒʹ͢Δ ϊʔυΛϋϒʹ͢Δ
1)VC.FEJBO-PDBUJPO.PEFM ֓ཁ w త͕ؔઢܗͷϞσϧ w ઢܗͰ͋ΔͨΊɼٻղ͍͢͠ʢઢܗ࠷దԽͱͯ͠ݫີղΛग़ͤΔʣ w ෳͷϋϒۭߓʹଓՄೳ w ඇϋϒͷۭߓಉ࢜Ͱͷଓͳ͍
ఏҊ͢ΔϞσϧ ֓ཁ త͕ؔ ઢܗ͔ ෳͷϋϒଓՄ ೳ͔ ϋϒͰͳ͍ ۭߓಉ࢜Ͱ ଓՄೳ͔ 1)VC.FEJBO
.PEFM ઢܗ Մೳ ෆՄ ఏҊ͢Δ Ϟσϧ ઢܗ Մೳ ʢ͖݅Ͱʣ Մೳ
ఏҊ͢ΔϞσϧ ఆࣜԽ w ఆࣜԽͷͨΊʹɼ৽ͨͳมΛ͍͔ͭ͘ఆٛ͢Δ w ϋϒۭߓ Λܦ༝͢Δɼۭߓ ͔Βۭߓ ίετ w
͢ͳΘͪɼ w ۭߓ ͔Βۭߓ ͷधཁͷ͏ͪɼϋϒۭߓ Λܦ༝͢Δׂ߹ w ͢ͳΘͪɼ w ϋϒۭߓΛܦ༝ͤͣɼۭߓ ͔Βۭߓ ߦׂ͘߹Λ ͱ͢Δ Ckm ij vk , vm i j Ckm ij = Cik + αCkm + Cmj Zkm ij i j vk , vm Zkm ij = hkm ij /hij i j Zij
ఏҊ͢ΔϞσϧ ఆࣜԽ w ͜ͷϞσϧ࣍ͷΑ͏ʹ࠷దԽͱͯ͠ఆࣜԽͰ͖Δ తؔ ੍݅ min ∑ i
∑ j (∑ k ∑ m Ckm ij hij Zkm ij + Cij hij Zij) ∑ j Xj = p ∀i, j; ∑ k ∑ m Zkm ij + Zij = 1 ∀i, j, k, m; 0 ≤ Zkm ij ≤ xm , xk ∀k; Xk ∈ {0,1}
ఏҊ͢ΔϞσϧ ࣮ߦ w ఆࣜԽͨ͠࠷దԽΛཧ࠷దԽιϧόʔ(VSPCJΛ༻͍ͯղΛٻΊΔ w (VSPCJཧ࠷దԽʢઢܗܭըɼ੍࣍ͳͲʣΛߴʹٻղ͢Δ w σʔλਓతʹཚΛ༻͍ͯ࡞ͨ͠
ఏҊ͢ΔϞσϧ ࣮ߦ݁Ռ w ٻղ͢ΔϓϩάϥϜΛ࡞ɼ࣮ߦ͢ΔͱӈਤͷΑ͏ͳωοτϫʔΫ͕ग़ྗ͞Ε Δɽ w ιʔείʔυ(JU)VC্ʹܝࡌ w 6TFS0LBCF+VOZB w
3FQP4QFDJBM4FNJOBS w ϋϒۭߓΛ৭Ͱग़ྗ w ඇϋϒͷۭߓಉ࢜݁Ε͍ͯΔ͜ͱ͕Θ͔Δ ࣮ߦ݁Ռ
·ͱΊ w ϋϒஔ࠷దԽʹ͍ͭͯطଘͷओཁͳख๏Λௐࠪ͠ɼͦͷ֦ுΛߦͬͨ w ͖݅Ͱඇϋϒͷۭߓಉ࢜ͷଓΛՄೳʹͨ͠ϞσϧΛఏҊͨ͠ w ඇϋϒಉ࢜Ͱͷଓ͕ՄೳͰ͋ΔͨΊɼݱ࣮ͷߤۭωοτϫʔΫʹΑΓۙ͠ ͍ωοτϫʔΫͱͳ͍ͬͯΔ w ࠓޙͷ՝ͱͯ͠ɼ࣮ࡍͷσʔλΛͱʹϋϒஔΛߦ͏͜ͱɼԆΓ
͑ͳͲͷίετΛՃຯͨ͠Ϟσϧͷ࡞ͳͲ͕ڍ͛ΒΕΔ