代教的および確率的手法による離散構造の限界の究明

• Project/Area Number: 16092205
• Research Category: Grant-in-Aid for Scientific Research on Priority Areas
• Allocation Type: Single-year Grants
• Review Section: Science and Engineering
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: 伊東 利哉 Tokyo Institute of Technology, 学術国際情報センター, 教授 (20184674)
• Co-Investigator(Kenkyū-buntansha): 上野 修一 東京工業大学, 大学院・理工学研究科, 教授 (30151814)
• Project Period (FY): 2004 – 2007
• Project Status: Completed (Fiscal Year 2007)
• Budget Amount: ¥13,800,000 (Direct Cost: ¥13,800,000); Fiscal Year 2007: ¥2,600,000 (Direct Cost: ¥2,600,000); Fiscal Year 2006: ¥3,600,000 (Direct Cost: ¥3,600,000); Fiscal Year 2005: ¥3,700,000 (Direct Cost: ¥3,700,000); Fiscal Year 2004: ¥3,900,000 (Direct Cost: ¥3,900,000)
• Keywords: 最小値独立置換族 / 代数的手法 / 確率的手法 / 最適選好マッチング / 商品価格設定問題 / VLSI計算 / 可逆計算 / 耐故障計算 / アルゴリズム / 情報基礎 / 数理工学 / 応用数学 / ラムゼー数 / オンラインアルゴリズム / 競合比 / 近似アルゴリズム / 直交描画 / 可逆論理回路 / 最小完全テスト集合 / ε-近似k-対独立置換族 / カップリング法 / 多項式近似スキーム / 逐次耐故障診断 / 確率的耐故障診断

Research Abstract

本研究では、代数的手法および確率的手法を用いて、置換族の構成、電子商取引、 VLSI計算、可逆計算、および耐故障計算などに関する離散構造の限界を解明した、置換族の構成に関しては、電子文書間の高速な類似性ツールとして応用が知られているκ限定ε近似的最小値独立置換族Fに対して、一般分布上で定義される置換族Fを行列Uにより定式化し、その行列Uの階数を評価することにより置換族Fのサイズの良好な下界を導出した。電子商取引に関しては、最適選好マッチング問題において、顧客集合が複数の重み付きグループに分割されているとき、顧客数n商品数mの比に関して、乱択化最適選好マッチングが存在するためのほほ合致する上界と下界を導出した(これは、既に知られている顧客集合が1つグループである場合の乱択化最適選好マッチングが存在するための顧客数nと商品数mの比に関する上界・下界の拡張である)。まだ、商品価格設定問題に関しては、正価格モデルおよび無損失割引モデルにおいて見積価格が制限された場合に対して、確率的手法を用いることで,グラフ価格設定問題・線状高速道路問題・環状高速道路問題の良好な近似アルゴリズムを提案した。VLSI計算に関しては、3次元チャネル配線問題がNP困難であることを明らかにした。可逆計算に関しては、可逆回路の縮退故障に対する最小完全テスト集合生成問題がNP困難であることを示した。耐故障計算に関しては、様々なネ ットワークに対して効率的な確率的耐故障ネットワークを構成する統一的な手法を提案した。

Research Products

• [Journal Article] Improved Approximation Algorithms for Item Pricing with Bounded Degree and Valuation (2008)
  • Author(s): R. Hamane and T, Itoh
  • Journal Title: IEICE Transactions on Information and Systems E91-D(2) Pages: 187-199
  • NAID: 110006272809
  • Peer Reviewed
• [Journal Article] On (ε,κ)-Min-Wise Independent Permutations (2007)
  • Author(s): N. Alon, T.I toh, and T. Nagatani
  • Journal Title: Random Structures and Algorithms Vol.31(3) Pages: 384-389
  • Peer Reviewed
• [Journal Article] On the Complexity of Three-Dimensional Channel Routing (2007)
  • Author(s): S. Tayu and S. Ueno
  • Journal Title: IEEE International Symposium on Circuits and Systems Pages: 3399-3402
  • NAID: 170000171227
  • Peer Reviewed
• [Journal Article] On the Fault testing for Reversible Circuits (2007)
  • Author(s): S. Tayu, S. Ito, and S. Ueno
  • Journal Title: Lecture Notes in Computer Science 4835 Pages: 812-821
  • Peer Reviewed
• [Journal Article] Primal-Dual Bounds of Linear Codes with Application to Cryptography (2006)
  • Author(s): R.Matsumoto, K.Kurosawa, T.Itoh, T.Konno, T.Uematsu
  • Journal Title: IEEE Transactions on Information Theory 12(9) Pages: 4251-4256
• [Journal Article] Competitive Analysis of Multi-Queue Preemptive QoS Algorithms for General Priorities (2006)
  • Author(s): T.Itoh, N.Takahashi
  • Journal Title: IEICE Transactions on Fundamentals E89-A(5) Pages: 1186-1197
• [Journal Article] Improved Lower Bounds for Families of ε-Approximate k-Restricted Min-wise Independent Permutations (2006)
  • Author(s): Toshiya Itoh
  • Journal Title: Electronic Colloquium on Computational Complexity TR06[17] Pages: 1-10
• [Journal Article] Improved Lower Bounds for Families oif ε-Approximate k-Restricted Min-wise Independent Permutations (2006)
  • Author(s): Toshiya Itoh, Tatsuya Nagatani
  • Journal Title: IEICE Technical Report COMP05[66] Pages: 23-30
• [Journal Article] Competitive Analysis of Multi-Queue Preemptive QoS Algorithms for General Priorities (2006)
  • Author(s): Toshiya Itoh, Noriyuki Takahashi
  • Journal Title: IEICE Trans.Fundamentals E98-A[5](To Appear)
• [Journal Article] A Note on the Complexity of Scheduling for Precedence Constrained Messages in Distributed Systems (2006)
  • Author(s): Koji Goda, Toshinori Yamada, Shuichi Ueno
  • Journal Title: IEICE Trans.Fundamentals E88-A[4] Pages: 1090-1092
  • NAID: 170000168113
• [Journal Article] On the Two-Dimensional Orthogonal Drawing of Series-Parallel Graphs (2006)
  • Author(s): Satoshi Tayu, Kumiko Nomura, Shuichi Ueno
  • Journal Title: IEICE Technical Report 105[502] Pages: 7-12
• [Journal Article] Improved Lower Bounds for Competitive Ratio of Multi-Queue Switches in QoS Networks (2005)
  • Author(s): T.Itoh, T.Nagumo
  • Journal Title: IEICE Trans.Fundamentals E88-A[5] Pages: 1155-1165
  • NAID: 110003178826
• [Journal Article] Primal-Dual Distance Bounds of Linear Codes With Application to Cryptography (2005)
  • Author(s): Ryutaroh Matsumoto, Kaoru Kurosawa, Toshiya Itoh
  • Journal Title: International Association for Cryptographic Research 194 Pages: 1-9
• [Journal Article] A Note on the Implementation of de Bruijn Networks by the Optical Transpose Interconnection System (2005)
  • Author(s): Kohsuke Ogata, Toshinori Yamada, Shuichi Ueno
  • Journal Title: IEICE Trans.Fundamentals E88-A[6] Pages: 3361-3662
• [Journal Article] On the Orthogonal Drawing of Outerplannar Graphs (2005)
  • Author(s): Kumiko Nomura, Satoshi Tayu, Shuichi Ueno
  • Journal Title: IEICE Trans.Fundamentals E88-A[6] Pages: 1583-1588
• [Journal Article] On VLSI Decompositions for d-ary de Bruijn Graphs (Extended Abstract) (2005)
  • Author(s): Toshinori Yamada, Hiroyuki Kawakita, Tadashi Nishiyama, Shuichi Ueno
  • Journal Title: Proceedings of the IEEE International Symposium on Circuits and Systems Pages: 1358-1361
• [Journal Article] On the Three-Dimensional Channel Routing (2005)
  • Author(s): Satoshi Tayu, Patrik Hurtig, Yoshiyasu Horikawa, Shuichi Ueno
  • Journal Title: Proceedings of the IEEE International Symposium on Circuits and Systems Pages: 180-183
• [Journal Article] On the Two-Dimensional Orthogonal Drawing of Series-Parallel Graphs (2005)
  • Author(s): Satoshi Tayu, Kumiko Nomura, Shuichi Ueno
  • Journal Title: IEICE Technical Report 105[387] Pages: 51-56
• [Journal Article] On the Complexity of Fault Testing for Reversible Circuits (2005)
  • Author(s): Shigeru Ito, Yusuke Ito, Satoshi Tayu, Shuichi Ueno
  • Journal Title: IEICE Technical Report 105[387] Pages: 13-16
• [Journal Article] Improved Lower Bounds for Competitive Ratio of Multi-Queue Switches in QoS Networks (2005)
  • Author(s): T.Itoh, T.Nagumo
  • Journal Title: 電子情報通信学会英文論文誌[A] (掲載予定)
  • NAID: 110003178826
• [Journal Article] On Sequential Diagnosis of Multiprocessor Systems (2005)
  • Author(s): T.Yamada, T.Ohtsuka, A.Watanabe, S.Ueno
  • Journal Title: Discrete Applied Mathematics 146 Pages: 311-342
  • NAID: 110003300176
• [Journal Article] Cost-Constrained Minimum-Delay Multicasting (2005)
  • Author(s): S.Tayu, T.Ghazi Al-Mutairi, S.Ueno
  • Journal Title: Lecture Notes in Computer Science 3381 Pages: 330-339
  • NAID: 110003281530
• [Journal Article] Explicit Construction of k-Wise Nearly Random Permutations by Iterated Feistel Transform (2004)
  • Author(s): T.Itoh, T.Nagatani, J.Tarui
  • Journal Title: 電子情報通信学会技術研究報告 7 Pages: 45-52
• [Journal Article] On the Orthogonal Drawing of Outerplannar Graphs (2004)
  • Author(s): K.Nomura, S.Tayu, S.Ueno
  • Journal Title: Lecture Notes in Computer Science 3106 Pages: 300-308
• [Journal Article] Sparse Networks Tolerating Random Faults (2004)
  • Author(s): T.Yamada, K.Nomura, S.Ueno
  • Journal Title: Discrete Applied Mathematics 137 Pages: 223-235
  • NAID: 110002812160
• [Presentation] On the Permutation Routing in All-optical Caterpillar Networks (2007)
  • Author(s): A. M. S. Shrestha, S. Tayu, and S. Ueno
  • Organizer: IEICE Technical Report
  • Place of Presentation: 新潟
  • Year and Date: 2007-11-29
• [Presentation] On the Fault Testing for Reversible Circuits (2007)
  • Author(s): S. Tayu, S. Ito, and S. Ueno
  • Organizer: IPSJ SIG Technical Reports
  • Place of Presentation: 京都
  • Year and Date: 2007-07-03
• [Presentation] Weighted Random Popular Matchings (2007)
  • Author(s): T. Itoh and O. Watanabe
  • Organizer: IEICE Technical Report
  • Place of Presentation: 札幌
  • Year and Date: 2007-06-29
• [Presentation] Improved Approximation Algorithms for Item Pricing with Bounded Degree and Valuation (2007)
  • Author(s): R. Hamane and T. Itoh
  • Organizer: IEICE Technical Report
  • Place of Presentation: 京都
  • Year and Date: 2007-04-26
• [Book] 情報基礎数学} (2007)
  • Author(s): 佐藤泰介, 高橋篤司, 伊東利哉, 上野修一
  • Total Pages: 222
  • Publisher: 昭晃堂