近接性を考慮した定数次数構造化オーバレイネットワーク

Masters Thesis Defence

1. ۙ઀ੑΛߟྀͨ͠ ఆ਺࣍਺ߏ଄ԽΦʔόϨΠωοτϫʔΫ നੴ ༟ً ಸྑઌ୺Պֶٕज़େֶӃେֶ ৘ใՊֶݚڀՊ ৘ใՊֶઐ߈ αΠόʔϨδϦΤϯεߏ੒ֶݚڀࣨ ത࢜લظ՝ఔ ฏ੒30೥౓ ത࢜લظ՝ఔ म࢜࿦จɾ՝୊ݚڀൃදձ 2019೥2݄12೔ 0VUHSPX
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2. ߏ଄ԽΦʔόϨΠωοτϫʔΫ • ΞϓϦέʔγϣϯϨϕϧͷ࿦ཧωοτϫʔΫ ‣ ID ʹجͮ͘ωοτϫʔΫ্ͷ୳ࡧΛ࣮ݱ - Chord [1] Λ͸͡Ίͱ͢Δଟ਺ͷϓτϩίϧ͕ଘࡏ - ୳ࡧΫΤϦͷసૹճ਺͸ϊʔυ਺ n ʹରͯ͠ O(log n) ‣ εέʔϥϏϦςΟͷߴ͍෼ࢄσʔλϕʔεΛ࣮ݱ - ྫ: ෼ࢄϋογϡද 2 [1] I. Stoica et al., “Chord: A Scalable Peer-to-peer Lookup Service for Internet Applications,” IEEE Trans. Netw., vol. 11, no. 1, pp. 17–32, 2003. ୲౰ϊʔυ ID IP ΞυϨε 10 203.0.113.6 2 198.51.100.2 ϊʔυ 21 ͷܦ࿏ද 21 10 2
3. ߏ଄ԽΦʔόϨΠͷਐา • ॳظͷߏ଄ԽΦʔόϨΠ (e.g., Chord) ‣ ֤ϊʔυ͸ద੾ͳྡ઀ϊʔυΛ O(log n) ͚ͩબ୒ͯ͠อ࣋ ‣ άϦʔσΟʔϧʔςΟϯάʹΑΓ O(log n) ϗοϓͰ୳ࡧ • ఆ਺࣍਺ߏ଄ԽΦʔόϨΠ ‣ ਖ਼ଇάϥϑͷߏ଄ʹجͮ͘ఆ਺ݸͷྡ઀ϊʔυΛอ࣋ ‣ ਖ਼ଇάϥϑ্ͷϧʔςΟϯάʹΑΓ O(log n) ϗοϓͰ୳ࡧ 3 Chord ͷτϙϩδ de Bruijn άϥϑ [
4. ਖ਼ଇάϥϑͱఆ਺࣍਺ߏ଄ԽΦʔόϨΠ • ωοτϫʔΫτϙϩδʹ๬·͍͠άϥϑతੑ࣭ ‣ ௚ܘ͕খ͍͞ = ܦ࿏௕͕খ͍͞ ‣ ࣍਺͕খ͍͞ = ܦ࿏දͷҡ࣋ίετ͕௿͍ ‣ ࿈݁ੑ͕ߴ͍ = ଱ো֐ੑ͕ߴ͍ ‣ ϧʔςΟϯάΞϧΰϦζϜ͕୯७ = ܦ࿏ܭࢉ͕ߴ଎ • ਖ਼ଇάϥϑͷதͰ΋ de Bruijn άϥϑ΍ Kautz άϥϑ͸্هͷ ੑ࣭ͷଟ͘Λຬͨ͢ ‣ ఆ਺࣍਺ߏ଄ԽΦʔόϨΠ: Koorde [2]ɺSKY [3] 4 [2] M. F. Kaashoek and D. R. Karger, “Koorde: A Simple Degree-Optimal Distributed Hash Table,” in Peer-to-Peer Systems II, 2003, pp. 98–107. [3] Y. Zhang, X. Lu, and D. Li, “SKY: Efficient Peer-to-Peer Networks Based on Distributed Kautz Graphs,” Sci. China Ser. F Inf. Sci., vol. 52, no. 4, pp. 588–601, Apr. 2009.
5. ΦʔόϨΠͷ࣮༻্ͷ໰୊఺ • ྡ઀ϊʔυ͸ԼҐωοτϫʔΫͱ͸ແؔ܎ʹܾఆ ‣ ஗Ԇͷେ͖ͳϊʔυͱͷ௨৴͕සൃ - ྫ: େ཮Λ·͙ͨ௨৴ ‣ ୳ࡧ஗Ԇͷ૿େ • ϊʔυؒͷۙ઀ੑΛߟྀͯ͠୳ࡧܦ࿏΍ ྡ઀ϊʔυΛબ୒ͯ͠୳ࡧ஗ԆΛ௿ݮ ‣ ۙ઀ܦ࿏બ୒ (PRS) [4] ‣ ۙ઀ྡ઀ϊʔυબ୒ (PNS): LPRS-Chord [5] 5 [4] K. Gummadi, et al., “The Impact of DHT Routing Geometry on Resilience and Proximity,” In Proc. 2003 Conf. on App., Tech., Arch., and Proto. for Computer Comm., 2003, pp. 381–394. [5] H. Zhang, A. Goel, and R. Govindan, “Incrementally Improving Lookup Latency in Distributed Hash Table Systems,” SIGMETRICS Perform. Eval. Rev., vol. 31, no. 1, pp. 114–125, Jun. 2003. ΦʔόϨΠ ωοτϫʔΫ ԼҐωοτϫʔΫ ೔ຊ ถࠃ
6. ఆ਺࣍਺ΦʔόϨΠʹ͓͚Δۙ઀ੑͷߟྀ • ఆ਺࣍਺ΦʔόϨΠ͸ਖ਼ଇάϥϑͷߏ଄ʹج͍ͮͯߏங (a) ௚ܘΛ࠷খԽ͢Δܦ࿏͸ͨͩͻͱͭ = ܦ࿏ʹࣗ༝౓͕ͳ͍ (= PRS Λద༻ෆՄ) (b) ྡ઀ϊʔυ͸ݫີʹܾఆ͞Ε͍ͯΔ = ྡ઀ϊʔυʹࣗ༝౓͕ͳ͍ (= PNS Λద༻ෆՄ) 6 [ [ (a) ϧʔςΟϯάΞϧΰϦζϜʹैΘͳ͍࣍ϗοϓ͸ ܦ࿏௕ͷ૿େΛҾ͖ى͜͢ (b) ਖ਼ଇάϥϑͷߏ଄ʹैΘͳ͍ϊʔυΛྡ઀ϊʔυͱ͢Δ ͜ͱ͸௚ܘͷ૿େɺ͋Δ͍͸౸ୡੑͷ૕ࣦΛҾ͖ى͜͢
7. ݚڀͷ໨తͱΞϓϩʔν • ఆ਺࣍਺ΦʔόϨΠʹ͓͍ͯϊʔυؒͷۙ઀ੑΛߟྀ͢Δ͜ͱ ʹΑΓ୳ࡧ஗Ԇͷ௿ݮΛ࣮ݱ ‣ ෼ࢄϥΠϯάϥϑ [6] ʹجͮ͘ఆ਺࣍਺ΦʔόϨΠͷτϙϩ δͷ֦େɾॖখͷࡍʹϊʔυؒͷۙ઀ੑͷߟྀ͕Մೳ ‣ ఏҊख๏ʮۙ઀ੑΛߟྀͨ͠෼ࢄϥΠϯάϥϑʯ - ۙ઀ੑΛߟྀͨ͠ఆ਺࣍਺ΦʔόϨΠͷߏஙख๏ 7 τϙϩδͷՄೳੑશମ͔Βۙ઀ੑʹج͍ͮͯ࠷దͳτϙϩδΛબ୒ [6] Y. Zhang and L. Liu, “Distributed Line Graphs: A Universal Technique for Designing DHTs Based on Arbitrary Regular Graphs,” IEEE Trans. Knowl. Data Eng., vol. 24, no. 9, pp. 1556–1569, Sep. 2012.
8. • ఆ਺࣍਺ΦʔόϨΠΛߏங͢ΔͨΊʹఏҊ͞Εͨ༗޲άϥϑ • ෼ࢄϥΠϯ൓෮ͱϊʔυ༥߹ɾ෼ׂʹΑΓಘΒΕΔ • d-ਖ਼ଇͳॳظάϥϑ͔ΒಘΒΕΔ෼ࢄϥΠϯάϥϑ͸ϊʔυͷ ࢀՃɾ཭୤ޙͷΦʔόϨΠτϙϩδʹରԠ • ෼ࢄϥΠϯάϥϑ͸ॳظωοτϫʔΫͷߏ଄Λҡ࣋ ‣ ೚ҙͷਖ਼ଇάϥϑʹجͮ͘ఆ਺࣍਺ΦʔόϨΠ͕ߏஙՄೳ ‣ ྫ: Kautz άϥϑʹجͮ͘ DLG-Kautz [3] 8 ෼ࢄϥΠϯάϥϑ [7], [8] [7] Y. Zhang and L. Liu, “Distributed Line Graphs: A Universal Technique for Designing DHTs Based on Arbitrary Regular Graphs,” IEEE Trans. Knowl. Data Eng., vol. 24, no. 9, pp. 1556–1569, Sep. 2012. [8] A. Manada and H. Morita, “Graph Theoretical Analysis on Distributed Line Graphs for Peer-to-Peer Networks,” IEEE Trans. Netw. Sci. Eng., pp. 1–1, 2018. [3] Y. Zhang, X. Lu, and D. Li, “SKY: Efficient Peer-to-Peer Networks Based on Distributed Kautz Graphs,” Sci. China Ser. F Inf. Sci., vol. 52, no. 4, pp. 588–601, Apr. 2009.
9. 1. ෼ࢄϥΠϯ൓෮: d ݸͷϊʔυ (ܑఋϊʔυ) Λੜ੒͢Δૢ࡞ 2. ϊʔυ༥߹: ෳ਺ͷϊʔυΛͻͱͭͷϊʔυʹ༥߹ ϊʔυͷࢀՃ − ୲౰ϊʔυͷ༥߹਺͕ 1 ͷ৔߹ 9 0 1 3 2 10 20 30 ୲౰ϊʔυ͔Βੜ੒͞Εܑͨఋϊʔυ ࢀՃͷ୲౰ϊʔυ 10 20 ࢀՃϊʔυ ܑఋϊʔυ ͷҰ෦ 30 10 (20) ࢀՃϊʔυ ୲౰ϊʔυ 30
10. ϊʔυͷࢀՃ − ୲౰ϊʔυͷ༥߹਺͕ 2 Ҏ্ͷ৔߹ 10 1. ϊʔυ෼ׂ: ༥߹͞Ε͍ͯΔϊʔυΛෳ਺ͷϊʔυʹ෼ׂ 10 (20) ࢀՃͷ୲౰ϊʔυ 10 20 ୲౰ϊʔυ ࢀՃϊʔυ
11. ۙ઀ੑΛߟྀͨ͠෼ࢄϥΠϯάϥϑ • ϊʔυ෼ׂ (༥߹) ͷํ๏ʹ͸ෳ਺ͷύλʔϯ͕ଘࡏ ‣ ϊʔυ͕ࢀՃͨ͠ޙͷτϙϩδʹෳ਺ͷՄೳੑ͕ଘࡏ ‣ ϊʔυؒͷۙ઀ੑΛߟྀͨ͠ϊʔυ෼ׂʹΑΓܾఆ - ྡ઀ϊʔυؒͷ௨৴஗ԆΛ௿ݮ - ϗοϓ͝ͱͷ஗ԆΛ௿ݮɺߴ଎ͳ୳ࡧΛ࣮ݱ 11 · · · <latexit sha1_base64="zuJOmAyo7rjOtrCBPhBytYpLsOA=">AAAB7XicdVDLSsNAFL3xWeur6tLNYBFchaQIuiy6cVnBPqAtZTKZtGMnmTBzI5TQf3DjQhG3/o87/8ZJW8HngWEO59zLvfcEqRQGPe/dWVpeWV1bL22UN7e2d3Yre/stozLNeJMpqXQnoIZLkfAmCpS8k2pO40DydjC+LPz2HddGqOQGJynvx3SYiEgwilZq9Vio0AwqVc+teQXIb+K7s9+rwgKNQeWtFyqWxTxBJqkxXd9LsZ9TjYJJPi33MsNTysZ0yLuWJjTmpp/Ptp2SY6uEJFLavgTJTP3akdPYmEkc2MqY4sj89ArxL6+bYXTez0WSZsgTNh8UZZKgIsXpJBSaM5QTSyjTwu5K2IhqytAGVLYhfF5K/ietmut7rn99Wq1fLOIowSEcwQn4cAZ1uIIGNIHBLdzDIzw5ynlwnp2XeemSs+g5gG9wXj8AtxWPNQ==</latexit> <latexit sha1_base64="zuJOmAyo7rjOtrCBPhBytYpLsOA=">AAAB7XicdVDLSsNAFL3xWeur6tLNYBFchaQIuiy6cVnBPqAtZTKZtGMnmTBzI5TQf3DjQhG3/o87/8ZJW8HngWEO59zLvfcEqRQGPe/dWVpeWV1bL22UN7e2d3Yre/stozLNeJMpqXQnoIZLkfAmCpS8k2pO40DydjC+LPz2HddGqOQGJynvx3SYiEgwilZq9Vio0AwqVc+teQXIb+K7s9+rwgKNQeWtFyqWxTxBJqkxXd9LsZ9TjYJJPi33MsNTysZ0yLuWJjTmpp/Ptp2SY6uEJFLavgTJTP3akdPYmEkc2MqY4sj89ArxL6+bYXTez0WSZsgTNh8UZZKgIsXpJBSaM5QTSyjTwu5K2IhqytAGVLYhfF5K/ietmut7rn99Wq1fLOIowSEcwQn4cAZ1uIIGNIHBLdzDIzw5ynlwnp2XeemSs+g5gG9wXj8AtxWPNQ==</latexit> <latexit sha1_base64="zuJOmAyo7rjOtrCBPhBytYpLsOA=">AAAB7XicdVDLSsNAFL3xWeur6tLNYBFchaQIuiy6cVnBPqAtZTKZtGMnmTBzI5TQf3DjQhG3/o87/8ZJW8HngWEO59zLvfcEqRQGPe/dWVpeWV1bL22UN7e2d3Yre/stozLNeJMpqXQnoIZLkfAmCpS8k2pO40DydjC+LPz2HddGqOQGJynvx3SYiEgwilZq9Vio0AwqVc+teQXIb+K7s9+rwgKNQeWtFyqWxTxBJqkxXd9LsZ9TjYJJPi33MsNTysZ0yLuWJjTmpp/Ptp2SY6uEJFLavgTJTP3akdPYmEkc2MqY4sj89ArxL6+bYXTez0WSZsgTNh8UZZKgIsXpJBSaM5QTSyjTwu5K2IhqytAGVLYhfF5K/ietmut7rn99Wq1fLOIowSEcwQn4cAZ1uIIGNIHBLdzDIzw5ynlwnp2XeemSs+g5gG9wXj8AtxWPNQ==</latexit> <latexit sha1_base64="zuJOmAyo7rjOtrCBPhBytYpLsOA=">AAAB7XicdVDLSsNAFL3xWeur6tLNYBFchaQIuiy6cVnBPqAtZTKZtGMnmTBzI5TQf3DjQhG3/o87/8ZJW8HngWEO59zLvfcEqRQGPe/dWVpeWV1bL22UN7e2d3Yre/stozLNeJMpqXQnoIZLkfAmCpS8k2pO40DydjC+LPz2HddGqOQGJynvx3SYiEgwilZq9Vio0AwqVc+teQXIb+K7s9+rwgKNQeWtFyqWxTxBJqkxXd9LsZ9TjYJJPi33MsNTysZ0yLuWJjTmpp/Ptp2SY6uEJFLavgTJTP3akdPYmEkc2MqY4sj89ArxL6+bYXTez0WSZsgTNh8UZZKgIsXpJBSaM5QTSyjTwu5K2IhqytAGVLYhfF5K/ietmut7rn99Wq1fLOIowSEcwQn4cAZ1uIIGNIHBLdzDIzw5ynlwnp2XeemSs+g5gG9wXj8AtxWPNQ==</latexit> ݱࡏͷτϙϩδ ϊʔυ෼ׂ τϙϩδͷՄೳੑશମ ۙ઀͢Δϊʔυ͕ΦʔόϨΠ্Ͱ ྡ઀͢ΔΑ͏ͳτϙϩδΛબ୒ ࢀՃϊʔυ ୲౰ϊʔυ
12. ϊʔυؒͷۙ઀ੑΛද͢ࢦඪ • ϊʔυ u, v ͷۙ઀ੑΛද͢ࢦඪ: ۙ઀ੑϝτϦοΫ [9] τ(u, v) ‣ τ(u, v) < τ(u, w) ͸ v ͕ w ΑΓ u ʹ͍ۙ͜ͱΛද͢ ‣ ϥ΢ϯυτϦοϓλΠϜͳͲ͔Βܭࢉ ‣ Ծఆ: ࣌ؒʹରͯ͠ෆมɺରশੑ (τ(u, v) = τ(v, u)) Λຬͨ͢ 12 [9] T. S. E. Ng, et al., “Measurement-Based Optimization Techniques for Bandwidth-Demanding Peer-to-Peer Systems,” in IEEE INFOCOM 2003., 2003, vol. 3, pp. 2199–2209 vol.3. τ(u, v) τ(u, w) u v w
13. ۙ઀ੑΛߟྀͨ͠ϊʔυ෼ׂ − ΞΠσΞ 13 9 > > > > > > > > > > > > > > > > > > = > > > > > > > > > > > > > > > > > > ; <latexit sha1_base64="YuPdThwNd5zVNLypTqBIG+4zDV8=">AAAClnicxVFNSwMxEM2u3/Wr2ovgJVgET8uuCNaLiEX0WMHaQreUbDrbBrPZJZmVlqU/yT/jzX9jWit+n30Q8nhvZjKZiTIpDPr+i+MuLC4tr6yuldY3Nre2yzu79ybNNYcmT2Wq2xEzIIWCJgqU0M40sCSS0Ioe6lO/9QjaiFTd4TiDbsIGSsSCM7RSr/wUSojRo2EEA6GKhKEWo0kpTKJ0VExoGP4TLYWg+h/taDEYYjjplau+d+xPQX+SwJvdfpXM0eiVn8N+yvMEFHLJjOkEfobdgmkUXIItnBvIGH9gA+hYqlgCplvMxjqhh1bp0zjV9iikM/VzRsESY8ZJZCNto0Pz3ZuKv3mdHONatxAqyxEUf3soziXFlE53RPtCA0c5toRxLWyvlA+ZZhztJkt2CO8/pX+T+2Mv8L3g9qR6UZuPY5XskwNyRAJySi7IDWmQJuFOxTlzLp26u+eeu1fu9Vuo68xzKuQL3MYrngDJlA==</latexit> <latexit sha1_base64="YuPdThwNd5zVNLypTqBIG+4zDV8=">AAAClnicxVFNSwMxEM2u3/Wr2ovgJVgET8uuCNaLiEX0WMHaQreUbDrbBrPZJZmVlqU/yT/jzX9jWit+n30Q8nhvZjKZiTIpDPr+i+MuLC4tr6yuldY3Nre2yzu79ybNNYcmT2Wq2xEzIIWCJgqU0M40sCSS0Ioe6lO/9QjaiFTd4TiDbsIGSsSCM7RSr/wUSojRo2EEA6GKhKEWo0kpTKJ0VExoGP4TLYWg+h/taDEYYjjplau+d+xPQX+SwJvdfpXM0eiVn8N+yvMEFHLJjOkEfobdgmkUXIItnBvIGH9gA+hYqlgCplvMxjqhh1bp0zjV9iikM/VzRsESY8ZJZCNto0Pz3ZuKv3mdHONatxAqyxEUf3soziXFlE53RPtCA0c5toRxLWyvlA+ZZhztJkt2CO8/pX+T+2Mv8L3g9qR6UZuPY5XskwNyRAJySi7IDWmQJuFOxTlzLp26u+eeu1fu9Vuo68xzKuQL3MYrngDJlA==</latexit> <latexit sha1_base64="YuPdThwNd5zVNLypTqBIG+4zDV8=">AAAClnicxVFNSwMxEM2u3/Wr2ovgJVgET8uuCNaLiEX0WMHaQreUbDrbBrPZJZmVlqU/yT/jzX9jWit+n30Q8nhvZjKZiTIpDPr+i+MuLC4tr6yuldY3Nre2yzu79ybNNYcmT2Wq2xEzIIWCJgqU0M40sCSS0Ioe6lO/9QjaiFTd4TiDbsIGSsSCM7RSr/wUSojRo2EEA6GKhKEWo0kpTKJ0VExoGP4TLYWg+h/taDEYYjjplau+d+xPQX+SwJvdfpXM0eiVn8N+yvMEFHLJjOkEfobdgmkUXIItnBvIGH9gA+hYqlgCplvMxjqhh1bp0zjV9iikM/VzRsESY8ZJZCNto0Pz3ZuKv3mdHONatxAqyxEUf3soziXFlE53RPtCA0c5toRxLWyvlA+ZZhztJkt2CO8/pX+T+2Mv8L3g9qR6UZuPY5XskwNyRAJySi7IDWmQJuFOxTlzLp26u+eeu1fu9Vuo68xzKuQL3MYrngDJlA==</latexit> <latexit sha1_base64="YuPdThwNd5zVNLypTqBIG+4zDV8=">AAAClnicxVFNSwMxEM2u3/Wr2ovgJVgET8uuCNaLiEX0WMHaQreUbDrbBrPZJZmVlqU/yT/jzX9jWit+n30Q8nhvZjKZiTIpDPr+i+MuLC4tr6yuldY3Nre2yzu79ybNNYcmT2Wq2xEzIIWCJgqU0M40sCSS0Ioe6lO/9QjaiFTd4TiDbsIGSsSCM7RSr/wUSojRo2EEA6GKhKEWo0kpTKJ0VExoGP4TLYWg+h/taDEYYjjplau+d+xPQX+SwJvdfpXM0eiVn8N+yvMEFHLJjOkEfobdgmkUXIItnBvIGH9gA+hYqlgCplvMxjqhh1bp0zjV9iikM/VzRsESY8ZJZCNto0Pz3ZuKv3mdHONatxAqyxEUf3soziXFlE53RPtCA0c5toRxLWyvlA+ZZhztJkt2CO8/pX+T+2Mv8L3g9qR6UZuPY5XskwNyRAJySi7IDWmQJuFOxTlzLp26u+eeu1fu9Vuo68xzKuQL3MYrngDJlA==</latexit> 10 (20) ୲౰ϊʔυ ࢀՃϊʔυ 10 20 ࢀՃϊʔυ ୲౰ϊʔυ 20 10 ࢀՃϊʔυ ୲౰ϊʔυ ग़ྡ઀ϊʔυ͸ͦΕͧΕ౳͍͠ ೖྡ઀ϊʔυ͸ͦΕͧΕҟͳΔ (A) (B) (B) (A) (A) (B)
14. ۙ઀ੑΛߟྀͨ͠ϊʔυ෼ׂ − ΞΠσΞ 14 9 > > > > > > > > > > > > > > > > > > = > > > > > > > > > > > > > > > > > > ; <latexit sha1_base64="YuPdThwNd5zVNLypTqBIG+4zDV8=">AAAClnicxVFNSwMxEM2u3/Wr2ovgJVgET8uuCNaLiEX0WMHaQreUbDrbBrPZJZmVlqU/yT/jzX9jWit+n30Q8nhvZjKZiTIpDPr+i+MuLC4tr6yuldY3Nre2yzu79ybNNYcmT2Wq2xEzIIWCJgqU0M40sCSS0Ioe6lO/9QjaiFTd4TiDbsIGSsSCM7RSr/wUSojRo2EEA6GKhKEWo0kpTKJ0VExoGP4TLYWg+h/taDEYYjjplau+d+xPQX+SwJvdfpXM0eiVn8N+yvMEFHLJjOkEfobdgmkUXIItnBvIGH9gA+hYqlgCplvMxjqhh1bp0zjV9iikM/VzRsESY8ZJZCNto0Pz3ZuKv3mdHONatxAqyxEUf3soziXFlE53RPtCA0c5toRxLWyvlA+ZZhztJkt2CO8/pX+T+2Mv8L3g9qR6UZuPY5XskwNyRAJySi7IDWmQJuFOxTlzLp26u+eeu1fu9Vuo68xzKuQL3MYrngDJlA==</latexit> <latexit sha1_base64="YuPdThwNd5zVNLypTqBIG+4zDV8=">AAAClnicxVFNSwMxEM2u3/Wr2ovgJVgET8uuCNaLiEX0WMHaQreUbDrbBrPZJZmVlqU/yT/jzX9jWit+n30Q8nhvZjKZiTIpDPr+i+MuLC4tr6yuldY3Nre2yzu79ybNNYcmT2Wq2xEzIIWCJgqU0M40sCSS0Ioe6lO/9QjaiFTd4TiDbsIGSsSCM7RSr/wUSojRo2EEA6GKhKEWo0kpTKJ0VExoGP4TLYWg+h/taDEYYjjplau+d+xPQX+SwJvdfpXM0eiVn8N+yvMEFHLJjOkEfobdgmkUXIItnBvIGH9gA+hYqlgCplvMxjqhh1bp0zjV9iikM/VzRsESY8ZJZCNto0Pz3ZuKv3mdHONatxAqyxEUf3soziXFlE53RPtCA0c5toRxLWyvlA+ZZhztJkt2CO8/pX+T+2Mv8L3g9qR6UZuPY5XskwNyRAJySi7IDWmQJuFOxTlzLp26u+eeu1fu9Vuo68xzKuQL3MYrngDJlA==</latexit> <latexit sha1_base64="YuPdThwNd5zVNLypTqBIG+4zDV8=">AAAClnicxVFNSwMxEM2u3/Wr2ovgJVgET8uuCNaLiEX0WMHaQreUbDrbBrPZJZmVlqU/yT/jzX9jWit+n30Q8nhvZjKZiTIpDPr+i+MuLC4tr6yuldY3Nre2yzu79ybNNYcmT2Wq2xEzIIWCJgqU0M40sCSS0Ioe6lO/9QjaiFTd4TiDbsIGSsSCM7RSr/wUSojRo2EEA6GKhKEWo0kpTKJ0VExoGP4TLYWg+h/taDEYYjjplau+d+xPQX+SwJvdfpXM0eiVn8N+yvMEFHLJjOkEfobdgmkUXIItnBvIGH9gA+hYqlgCplvMxjqhh1bp0zjV9iikM/VzRsESY8ZJZCNto0Pz3ZuKv3mdHONatxAqyxEUf3soziXFlE53RPtCA0c5toRxLWyvlA+ZZhztJkt2CO8/pX+T+2Mv8L3g9qR6UZuPY5XskwNyRAJySi7IDWmQJuFOxTlzLp26u+eeu1fu9Vuo68xzKuQL3MYrngDJlA==</latexit> <latexit sha1_base64="YuPdThwNd5zVNLypTqBIG+4zDV8=">AAAClnicxVFNSwMxEM2u3/Wr2ovgJVgET8uuCNaLiEX0WMHaQreUbDrbBrPZJZmVlqU/yT/jzX9jWit+n30Q8nhvZjKZiTIpDPr+i+MuLC4tr6yuldY3Nre2yzu79ybNNYcmT2Wq2xEzIIWCJgqU0M40sCSS0Ioe6lO/9QjaiFTd4TiDbsIGSsSCM7RSr/wUSojRo2EEA6GKhKEWo0kpTKJ0VExoGP4TLYWg+h/taDEYYjjplau+d+xPQX+SwJvdfpXM0eiVn8N+yvMEFHLJjOkEfobdgmkUXIItnBvIGH9gA+hYqlgCplvMxjqhh1bp0zjV9iikM/VzRsESY8ZJZCNto0Pz3ZuKv3mdHONatxAqyxEUf3soziXFlE53RPtCA0c5toRxLWyvlA+ZZhztJkt2CO8/pX+T+2Mv8L3g9qR6UZuPY5XskwNyRAJySi7IDWmQJuFOxTlzLp26u+eeu1fu9Vuo68xzKuQL3MYrngDJlA==</latexit> 10 (20) ୲౰ϊʔυ ࢀՃϊʔυ 10 20 ࢀՃϊʔυ ୲౰ϊʔυ 20 10 ࢀՃϊʔυ ୲౰ϊʔυ ग़ྡ઀ϊʔυ͸ͦΕͧΕ౳͍͠ ೖྡ઀ϊʔυ͸ͦΕͧΕҟͳΔ (A) (B) (B) (A) (A) (B) 1. ୲౰ϊʔυͱೖྡ઀ϊʔυؒ 2. ࢀՃϊʔυͱೖྡ઀ϊʔυؒ ͷ௨৴஗ԆΛ࠷దԽ͢ΔτϙϩδΛߏஙͯ͠ ֦େޙͷτϙϩδͱ͢Ε͹ྑ͍
15. ۙ઀ੑΛߟྀͨ͠ϊʔυ෼ׂ (1) 15 (A) (B) εςοϓ 1. ୲౰ϊʔυ p ͔Β༥߹ϊʔυ v ∈ {10, 20} ͷೖྡ઀ϊʔυ ΁ͷฏۉۙ઀ੑϝτϦοΫ Λܭଌ u ∈ N−(v) Tp (v) Tp (10) = ∑ u∈N−(10) τ(p, u) |N−(10)| = 15 Tp (20) = ∑ u∈N−(20) τ(p, u) |N−(20)| = 30 10 ୲౰ϊʔυ p τ(p, u) = 10 τ(p, u) = 20 τ(p, u) = 30 ୲౰ϊʔυ p 20
16. ۙ઀ੑΛߟྀͨ͠ϊʔυ෼ׂ (2) 16 (A) (B) Tq (20) = ∑ u∈N−(20) τ(q, u) |N−(20)| = 20 Tq (10) = ∑ u∈N−(10) τ(q, u) |N−(10)| = 20 20 ࢀՃϊʔυ q τ(q, u) = 20 τ(q, u) = 15 ࢀՃϊʔυ q 10 τ(q, u) = 25 εςοϓ 2. ࢀՃϊʔυ q ͔Β༥߹ϊʔυ v ∈ {10, 20} ͷೖྡ઀ϊʔυ ΁ͷฏۉۙ઀ੑϝτϦοΫ Λܭଌ u ∈ N−(v) Tq (v)
17. ۙ઀ੑΛߟྀͨ͠ϊʔυ෼ׂ (3) 17 εςοϓ 3. Λ ͷঢॱʹฒ΂ͯ࠷ॳͷ൒෼Λ ୲౰ϊʔυ pɺͦͯ͠࢒Γͷ൒෼ΛࢀՃϊʔυ q ʹ༥߹ v ∈ {10, 20} h(v) = Tp (v) − Tq (v) h(10) = Tp (10) − Tq (10) = 15 − 20 = − 5, h(20) = Tp (20) − Tq (20) = 30 − 20 = 10. 10 Λ pɺ20 Λ q ʹ༥߹ ୲౰ϊʔυ p ࢀՃϊʔυ q 10 20 20 ୲౰ϊʔυ p ࢀՃϊʔυ q 30 15 25
18. ۙ઀ੑΛߟྀͨ͠ϊʔυ෼ׂ (3) 18 εςοϓ 3. Λ ͷঢॱʹฒ΂ͯ࠷ॳͷ൒෼Λ ୲౰ϊʔυ pɺͦͯ͠࢒Γͷ൒෼ΛࢀՃϊʔυ q ʹ༥߹ v ∈ {10, 20} h(v) = Tp (v) − Tq (v) h(10) = Tp (10) − Tq (10) = 15 − 20 = − 5, h(20) = Tp (20) − Tq (20) = 30 − 20 = 10. 10 Λ pɺ20 Λ q ʹ༥߹ ୲౰ϊʔυ p ࢀՃϊʔυ q 10 20 20 ୲౰ϊʔυ p ࢀՃϊʔυ q 30 15 25 ఏҊख๏ʹΑΓߏங͞ΕΔ τϙϩδ
19. ධՁͷ४උ − ԼҐωοτϫʔΫτϙϩδͷੜ੒ (1) • ෳ਺ڌ఺͔ΒͳΔσʔληϯλΛ૝ఆ͠ɺτϥϯδοτελϒ Ϟσϧ [10] ʹج͍ͮͯԼҐωοτϫʔΫͷτϙϩδΛੜ੒ ‣ 5050 ୆ͷϧʔλʹΑΔ L3 ωοτϫʔΫτϙϩδ 19 transit node transit domain stub domain stub node [10] E. W. Zegura, K. L. Calvert and S. Bhattacharjee, "How to Model an Internetwork," In Proc. IEEE INFOCOM '96. Conference on Computer Communications, 1996, pp. 594-602 vol.2. τϥϯδοτυϝΠϯ τϥϯδοτ ϊʔυ ελϒυϝΠϯ ελϒϊʔυ
20. ධՁͷ४උ − ԼҐωοτϫʔΫτϙϩδͷੜ੒ (2) • GT-ITM Λར༻ͯ͠ϊʔυؒͷ௨৴஗ԆΛઃఆ͠ɺΦʔόϨΠ ͷϊʔυΛελϒϊʔυʹׂΓ౰ͯ ‣ ઃఆ͞ΕΔ௨৴஗Ԇͷ஋͸࣮ࡍͷΠϯλʔωοτͷ΋ͷΑ Γେ͖ͳ஋ͱͳΔ ‣ γϛϡϨʔγϣϯͰ͸ൺ཰ʹΑΔධՁΛߦ͏ 20 ελϒϊʔυؒͷ௨৴஗Ԇͷ֬཰ີ౓
21. ఏҊख๏ͷଥ౰ੑͷධՁ • ఏҊख๏͕ۙ઀ੑΛߟྀ͠ͳ͍΋ͷͱൺֱͯ͠୳ࡧ஗ԆΛ௿ݮ ͢Δ͜ͱΛࣔ͢ 1. ॳظάϥϑΛ d-ਖ਼ଇ׬શάϥϑͱ͢Δ෼ࢄϥΠϯάϥϑʹ جͮ͘ DLG-Kautz ͱఏҊख๏ʹجͮ͘ PDLG-Kautz Λߏங 2. ϥϯμϜʹબΜͩ 2 ͭͷϊʔυؒͷ୳ࡧΛ 106 ճߦ͍ɺ୳ ࡧ஗Ԇͱ֤ϊʔυʹ༥߹͞Ε͍ͯΔϊʔυͷ਺Λܭଌ • γϛϡϨʔγϣϯͷઃఆ ‣ ॳظάϥϑ d = 2, 16 ‣ ϊʔυ਺ N = 256, 512, 1024, ..., 65536 21
22. ୳ࡧ஗Ԇͱ༥߹਺ͷؔ܎ (d = 2) 22 ฏۉ୳ࡧ஗Ԇͱ֤ϊʔυʹ༥߹͞Ε͍ͯΔϊʔυ਺ͷฏۉ (d = 2) ϊʔυ਺ʹΑΒͣ ୳ࡧ஗ԆΛ10%ఔ౓௿ݮ
23. ୳ࡧ஗Ԇͱ༥߹਺ͷؔ܎ (d = 16) 23 ฏۉ୳ࡧ஗Ԇͱ֤ϊʔυʹ༥߹͞Ε͍ͯΔϊʔυ਺ͷฏۉ (d = 16)
24. ୳ࡧ஗Ԇͱ༥߹਺ͷؔ܎ (d = 16) 24 ฏۉ୳ࡧ஗Ԇͱ֤ϊʔυʹ༥߹͞Ε͍ͯΔϊʔυ਺ͷฏۉ (d = 16) ༥߹਺ͷ௿Լʹ൐ͬͯ ୳ࡧ஗Ԇͷ࡟ݮ཰͕ݮগ ୳ࡧ஗Ԇͷ࡟ݮ཰͸ ࠷େ10%ఔ౓
25. ྡ઀ϊʔυͷ௨৴஗ԆͷධՁ • ఏҊख๏͕ۙ઀ੑΛߟྀ͠ͳ͍΋ͷͱൺֱ֤ͯ͠ϊʔυͱͦͷ ग़ྡ઀ϊʔυؒͷ௨৴஗ԆΛ௿ݮ͢Δ͜ͱΛࣔ͢ 1. ॳظάϥϑΛ d-ਖ਼ଇ׬શάϥϑͱ͢Δ෼ࢄϥΠϯάϥϑʹ جͮ͘ DLG-Kautz ͱఏҊख๏ʹجͮ͘ PDLG-Kautz Λߏங 2. ֤ϊʔυͱͦͷग़ྡ઀ϊʔυؒͷ௨৴஗ԆΛܭଌ • γϛϡϨʔγϣϯͷઃఆ ‣ ॳظάϥϑ d = 2 ‣ ϊʔυ਺ N = 32768, 65536 25
26. ֤ϊʔυͱग़ྡ઀ϊʔυؒͷ௨৴஗Ԇͷ෼෍ (1) 26 ֤ϊʔυͱग़ྡ઀ϊʔυؒͷ௨৴஗Ԇͷ෼෍ (d = 2, N = 32768) ௨৴஗Ԇͷ෼෍͸ۙ઀ੑΛߟྀ͠ͳ͍ ΋ͷͱൺֱͯ͠ྑ͍
27. ֤ϊʔυͱग़ྡ઀ϊʔυؒͷ௨৴஗Ԇͷ෼෍ (2) 27 ֤ϊʔυͱग़ྡ઀ϊʔυؒͷ௨৴஗Ԇͷ෼෍ (d = 2, N = 65536) ϊʔυ਺ͷ૿Ճʹରͯ͠΋௨৴஗Ԇͷ ෼෍͸େ͖͘มԽ͠ͳ͍
28. ۙ઀ੑͷߟྀʹඞཁͳϝοηʔδ਺ͷఆੑධՁ • ఏҊख๏Ͱ͸ɺ༥߹͞Ε͍ͯΔϊʔυ͢΂ͯʹରͯ͠ฏۉۙ઀ੑϝ τϦοΫΛܭࢉ͢Δඞཁ͕͋Δ ‣ ༥߹ϊʔυͷೖ࣍਺͸͔͔ͨͩ d (म࢜࿦จͷఆཧ 2) ‣ ͻͱͭͷ༥߹ϊʔυʹ͍ͭͯۙ઀ੑϝτϦοΫͷܭଌʹඞཁͳ ϝοηʔδ਺͸ O(d) ‣ ֤ϊʔυʹ༥߹͞Ε͍ͯΔϊʔυ਺͸͔͔ͨͩ d (ܑఋϊʔυ਺) ‣ ͕ͨͬͯ͠ɺO(d 2) ͷϝοηʔδ͕ඞཁ (ϊʔυ਺ͱ͸ແؔ܎) 28 ༥߹ϊʔυ਺͸ ͔͔ͨͩ d ༥߹ϊʔυͷೖ࣍਺͸ ͔͔ͨͩ d
29. ·ͱΊͱࠓޙͷ՝୊ 29 ·ͱΊ • ՝୊ ఆ਺࣍਺ߏ଄ԽΦʔόϨΠʹ͓͚Δۙ઀ੑͷߟྀ • ఏҊ ෼ࢄϥΠϯάϥϑʹ͓͍ͯۙ઀ੑΛߟྀͨ͠ϊʔυ • ༥߹/෼ׂʹΑΓτϙϩδΛஞ࣍తʹ֦େ/ॖখ͢Δख๏ • ੒Ռ γϛϡϨʔγϣϯͰ͸୳ࡧ஗ԆΛ໿ 10% ௿ݮ ࠓޙͷ՝୊ • ϊʔυͷࢀՃ΍཭୤Ҏ֎ͷλΠϛϯάͰτϙϩδΛ࠷దԽ͢Δ ख๏ͷߟҊ