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2003 Fiscal Year Final Research Report Summary

High Quality Discrete Algorithms Based on Engineering Criteria

Research Project

Project/Area Number 13480081
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field 計算機科学
Research InstitutionKyoto University

Principal Investigator

IWAMA Kazuo  KYOTO UNIVERSITY, Graduate School of Informatics, Professor, 情報学研究科, 教授 (50131272)

Co-Investigator(Kenkyū-buntansha) MIYAZAKI Shuichi  KYOTO UNIVERSITY, Academic Center for Computing and Media Studies, Associate Professor, 学術情報メディアセンター, 助教授 (00303884)
ITO Hiro  KYOTO UNIVERSITY, Graduate School of Informatics, Associate Professor, 情報学研究科, 助教授 (50283487)
OKABE Yasuo  KYOTO UNIVERSITY, Academic Center for Computing and Media Studies, Professor, 学術情報メディアセンター, 教授 (20204018)
HORIYAMA Takashi  KYOTO UNIVERSITY, Graduate School of Informatics, Research Associate, 情報学研究科, 助手 (60314530)
Project Period (FY) 2001 – 2003
KeywordsDiscrete Algorithms / Discrete Optimization / Stable Marriage Problems / Approximation Algorithms / Online Algorithms / Satisfiability Problems / Computational Complexity / Network Algorithms
Research Abstract

Discrete algorithms have been evaluated by the unique measure 'asymptotic time complexity' for many cases. Recently, however, many other measures have been proposed, e.g., the approximation ratios for solving combinatorial problems approximately, and the competitive ratios for solving online problems in which we have no information on the future inputs. In this research, we studied these new measures as the criteria based on engineering requirements, and developed the methodologies for qualifying algorithms from this point of view.
As to the stable marriage problems, it is known to be solvable in polynomial time. We have generalized the problem, and proved that it is also solvable in polynomial time even when ties in the lists or incomplete lists are allowed. While we proved the intractability for the case both ties and incompleteness are allowed, we proposed an approximation algorithm that achieves an approximation ratio less than 2.
As to the satisfiability problems, we developed a 1.324^n algorithm for 3-SAT by complementarily combining two types of algorithms based on, the local search and the backtracking. We also considered condensing the density (i.e., the ratio of satisfying assignments to the 2^n assignments) of formulas.
Other research topics are as follows ; online algorithms, network algorithms, quantum algorithms.

  • Research Products

    (16 results)

All Other

All Publications (16 results)

  • [Publications] K.Iwata, Y.Okabe, T.Takase: "Separating Oblivious and Non-Oblivious BPs"Proc.Computing and Combinatorics Conference. 28-38 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] D.Manlove, R.Irving, K.Iwama, S.Miyazaki, Y.Morita: "Hard Variants of Stable Marriage"Theoretical Computer Science. 276/1. 261-279 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Halldorsson, K.Iwama, S.Miyazaki, S.Taketomi: "Online Independent Sets"Theoretical Computer Science. 289/2. 953-962 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Hanatani, T.Horiyama, K.Iwama: "Condensation of Boolean Formulas"Proc.DIMACS Workshop on Complexity and Inference. 126-133 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Ito, K.Iwama, Y.Okabe, T.Yoshihiro: "Polynomial Time Computable Backup Tables for Shortest Path Routing"Proc.the 10th International Colloquim on Structural Information and Communication Complexity. 17. 163-177 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 岩間一雄: "オートマトン・言語と計算理論(電子情報通信レクチャーシリーズB-6)"コロナ社. 172 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Iwama, Y.Okabe, T.Takase: "Separating Oblivious and Non-Oblivious BPs"Proc.Computing and Combinatorics Conference. 28-38 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] D.Manlove, R.Irving, K.Iwama, S.Miyazaki, Y.Morita: "Hard Variants of Stable Marriage"Theoretical Computer Science. vol.276/1. 261-279 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Halldorsson, K.Iwama, S.Miyazaki, S.Taketomi: "Online Independent Sets"Theoretical Computer Science. vol.289/2. 953-962 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Iwama, D.Kawai, S.Miyazaki, Y.Okabe, J.Umemoto: "Parallelizing Local Search for CNF Satisfiability Using Vectorization and PVM"ACM Journal of Experimental Algorithms. vol.7. Article 2 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Halldorsson, R.Irving, K.Iwama, D.Manlove, S.Miyazaki, Y.Morita, R.Scott: "Approximability Results for Stable Marriage Problems with Ties"Theoretical Computer Science. vol.306/1-3. 431-447 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Hanatani, T.Horiyama, K.Iwama: "Condensation of Boolean Formulas"Proc.DIMACS Workshop on Complexity and Inference. 126-133 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Ito, K.Iwama, Y.Okabe, T.Yoshihiro: "Polynomial Time Computable Backup Tables for Shortest Path Routing"Proc.the 10th International Colloquim on Structural Information and Communication Complexity. vol.17. 163-177 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Halldorsson, K.Iwama, S.Miyazaki, H.Yanagisawa: "Improved Approximation of the Stable Marriage Problem"Proc.the 11th Annual European Symposium on Algorithms, Lecture Notes in Computer Science. vol.2832. 266-277 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Iwama, S.Tamaki: "Improved Upper Bounds for 3-SAT"Proc.the 15th Annual ACM-SIAM Symposium on Discrete Algorithms. 321-322 (2004)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Iwama: "Automata, Languages and Theory of Computation (Tokyo)"Corona Publishing. 172 (2003)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2005-04-19  

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