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2000 Fiscal Year Final Research Report Summary

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
Keywordsgraph / network / matroid / Tutte polynomial / discrete system / network reliability / binary decision diagram / Jones polynomial
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.

  • Research Products

    (16 results)

All Other

All Publications (16 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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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

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Published: 2002-03-26  

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