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Discrete System Theory and Large-Scale Optimization Methods Based on Binary Decision Diagrams and

Research Project

Project/Area Number 09480050
Research Category

Grant-in-Aid for Scientific Research (B).

Allocation TypeSingle-year Grants
Section一般
Research Field 計算機科学
Research Institutionthe University of Tokyo

Principal Investigator

IMAI Hiroshi  Graduate School of Science, the University of Tokyo Assoc.Prof., 大学院・理学系研究科, 助教授 (80183010)

Co-Investigator(Kenkyū-buntansha) IWATA Satoru  Graduate School of Engineering, the University of Tokyo Assoc.Prof., 大学院・工学系研究科, 助教授 (00263161)
INABA Mary  Graduate School of Science, the University of Tokyo Lecturer, 大学院・理学系研究科, 講師 (60282711)
ASAI Ken-ichi  Graduate School of Science, the University of Tokyo Research Assistant, 大学院・理学系研究科, 助手 (10262156)
Project Period (FY) 1997 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥14,800,000 (Direct Cost: ¥14,800,000)
Fiscal Year 2000: ¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 1999: ¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 1998: ¥3,800,000 (Direct Cost: ¥3,800,000)
Fiscal Year 1997: ¥4,500,000 (Direct Cost: ¥4,500,000)
Keywordsgraph / network / matroid / Tutte polynomial / discrete system / network reliability / binary decision diagram / Jones polynomial / Tutte 多項式 / Jones 多項式 / Trtte多項式
Research Abstract

In this research, we aimed at proposing a unified approach to discrete system theory based on binary decision diagrams, and developing a prototype system for the unified system. By our results, we can now represent the whole moderate-scale discrete structure in a implicit and compact manner, which could not be done by the existing methods. We applied our approach to network reliability computation and also computing the Jones polynomial of a knot. These computation problems are known to be #P-hard, but, with our methods, moderate-size problems can be solved rigorously in practice. For example, the network reliability function of a grid of 14x14 can be computed. We also explore fundamental theory of binary decision diagrams, by investigating the difference in size when a monotone Boolean function is represented directly and when it is represented by their prime implicants.
New approaches have also been demonstrated, one is based on algebraic approach, and the other is based on quantum approach. Concerning the algebraic approach, Grobner bases are fully investigated for network flow problems. Concerning the quantum approach, we investigate a quantum analog of binary decision diagrams in order to investigate the computational power of quantum computing. These new results will be published soon.

Report

(5 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • 1998 Annual Research Report
  • 1997 Annual Research Report
  • Research Products

    (44 results)

All Other

All Publications (44 results)

  • [Publications] K.Sekine and H.Imai: "Counting the Number of Paths in a Graph via BDDs"IEICE Transactions on Fundamentals. E80-A,4. 682-688 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Imai,K.Sekine and K.Imai: "Network Reliability Computation-Theory and Practice"Proceedings of the IPSJ International Symposium on Information Systems and Technologies for Network Society. World Sci.. 41-48 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 関根京子,今井浩,今井桂子: "Jones多項式の計算"日本応用数理学会論文誌. 8,3. 341-354 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Hayase and H.Imai: "OBDDs of a Monotone Function and of Its Prime Implicants"Theory of Computing Systems. 31. 579-591 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Imai,K.Sekine and K.Imai: "Computational Investigations of All-Terminal Network Reliability via BDDs"IEICE Trans.Fundamentals. E82-A,5. 714-721 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Imai: "Computing the Invariant Polynomials of Graphs, Networks and Matroids"IEICE Trans.Information and Systems. E83-D,3. 330-343 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 藤重悟 編,今井浩 他著: "離散構造とアルゴリズムV:ネットワーク信頼度計算の周辺-組合せ数え上げの新展開"近代科学社. 1-50 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 浅野孝夫,今井浩: "計算とアルゴリズム"オーム社. 295 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Sekine and H.Imai: "Counting the Number of Paths in a Graph via BDDs"IEICE Transactions on Fundamentals. E80-A. 682-688 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Imai, K.Sekine and K.Imai: "Network Reliability Computation-Theory and Practice"Proceedings of the IPSJ International Symposium on Information Systems and Technologies for Network Society, World Sci.. 41-48 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Sekine, H.Imai and K.Imai: "Computation of the Jones Polynomial (in Japanese)"Trans.Of the Japan Society for Industrial and Applied Mathematics. 8, 3. 341-354 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Hayase and H.Imai: "OBDDs of a Monotone Function and of Its Prime Implicants"Theory of Computing Systems. 31. 579-591 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Imai, K.Sekine and K.Imai: "Computational Investigations of All-Terminal Network Reliability via BDDs"IEICE Trans.Fundamentals. E82-A, 5. 714-721 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Imai: "Computing the Invariant Polynomials of Graphs, Networks and Matroids"IEICE Trans.Information and Systems. E83-D, 3. 330-343 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] S.Fujishige, ed., H.Imai et al: "Discrete Structure and Algorithms V : Network Reliability Computation and Related Topics (in Japanese)"Kindai-kgaku-sha. 1-50 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Asano and H.Imai: "Computation and Algorithms (in Japanese)"Ohm-sha. 295 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 今井浩,関根京子: "ネットワークシステムの信頼性の定量的評価法"日本OR学会平成12年度秋期研究発表会アブストラクト集. 2-A-6. (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Yamasaki,H.Kobayashi,Y.Tokunaga and H.Imai: "One-Way Probabilistic Reversible and Quantum One-Counter Automata"Lecture Notes in Computer Science. 1858. 436-446 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Imai and M.Inaba: "Geometric Clustering by Divergence and Its Underlying Discrete Proximity Structures"IEICE Trans.Information and Systems. E83-D,1. 27-35 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] M.Inaba,N.Katoh and H.Imai: "Variance-Based κ-Clustering Algorithms by Voronoi Diagrams and Randomization"IEICE Trans.Information and Systems. E83-D,6. 1199-1206 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Imai,M.Hachimori,M.Hamada,H.Kobayashi and K.Matsumoto: "Optimization in Quantum Computation and Information"Proceedings of the 2nd Japanese-Hungarian Symposium on Discrete Mathematics. (4月出版予定). (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] J.Gruska and H.Imai: "Power, Puzzles and Properties of Entanglement"Lecture Notes in Computer Science. (5月出版予定). (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] H. Imai, K. Sekine and K. Imai: "Comutational Investigations of All-Terminal Nerwork Reliability via BDDs"IEICE Trans.Fundamentals. E82-A,5. 714-721 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 今井浩: "離散システム不変多項式と計算位相・幾何"日本数学家1999年度秋季総合分科会応用数学分科会特別講演. 44-56 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] A. Nagai and H. Imai: "Proof for the Equivlence Between Some Best-First Algorithms and Depth-First Algorithms for AND/OR Trees"Proceedings of the Korea-Japan Joint Workshop on Algorithms and Computation. 163-170 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 今井浩,関根京子: "グラフのTutte多項式計算システム"京都大学数理解析研究所講究録. 1120. 120-129 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 定兼邦彦,今井浩: "転置ファイルおよび接尾辞配列の効率的圧縮法"情報処理学会論文誌:データベース. 40,SIG8. 85-94 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] H. Imai: "Computing the Invariant Polynomials of Graphs, Networks and Matroids"IEICE Trans. Information and Systems. E83-D,3(印刷中). (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] T. Asano, H. Imai, D. T. Lee, S. Nakano, T. Tokuyama, eds.: "Computing and Combinatorics"Spriger-Verlag. 494 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 浅野孝夫,今井浩: "計算とアルゴリズム"オーム社. 295 (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] K.Hayase and H.Imai: "OBDDs of a Monotone Function and of Its Prlme Implicants" Theory of Computing Systems. vol.31. 579-591 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 関根京子、今井浩、今井桂子: "Jones多項式の計算" 日本応用数理学会論文誌. vol.8,No.3. 341-354 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Koji Hakata and Hiroshi Imai: "Algorithms for the Longest Comma,Subsequence Boblam for Multiple Strings Based on Gemetric Maxima" Optimization Methods and Software. vol.10. 233-260 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Inaba and H.Imai: "Geometric Clustering in Feature Space" Lecture Notes in Artificial Intelligence. vol.1532. 421-422 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] A.Tajima and H.Imai: "Computational Investigations of the Optimality of Two-and Three-Dimensional Triangulations under Several Criteria" Proceedings of the 10th Canadian Conference on Computational Geometry. 44-45 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Imai,K.Sekine and K.Imai: "Computational Investigations of All-Terminal Network Reliability via BDDs" IEICE Trans Fundamentals. vol.E82A.No.5(掲載予定). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 今井 浩: "ネットワーク信頼度計算の周辺-組合せ数え上げの新展開 離散構造とアルゴリズムV(藤重悟編)" 近代科学社, 50 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Sekine and H.Imai: "Counting the Number of Paths in a Graph via BDDs." IEICE Transactions on Fundamentals. Vol.E80-A No.4. 682-688 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Imai, K.Sekine and K.Imai: "Network Reliability Computation-Theory and Practice." Proc.IPSJ Int.Symp on Information Systems and Technologies for Network Society. 41-48 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Imai: "Parametric and Sensitivity Analysis of Network Reliability" 5th Int.Conf.on Parametric Optimization and Related Topics. 5A4. 68 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] F.Takeuchi and H.Imai: "Enumerating Triangulations for Products of Two Simplices and for Arbitrary Configurations of Points." Lecture Notes in Computer Science. Vol.1276. 470-481 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] K.Onishi and H.Imai: "Voronoi Diagrams for an Exponential Family of Probability Distributions in Information Geometry." Japna-Korea Joint Workshop on Algorithms and Computation. 1-8 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] K.Hayase and H.Imai: "OBDDs of a Monotone Function and of Its Prime Implicants" Theory of Computing Systems. (1998,発表予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] 今井 浩: "ネットワーク信頼度計算の周辺-組合せ数え上げの新展開.離散構造とアルゴリズムV(藤重悟編)" 近代科学社(発表予定), 1-50 (1998)

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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