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Analyses of Randomized Algorithms for Constraint Satisfaction Problems

Research Project

Project/Area Number 13680400
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 計算機科学
Research InstitutionTokyo Institute of Technology

Principal Investigator

WATANABE Osamu  Tokyo Institute of Technology, Graduate School of Information Science and Engineering, Professor, 大学院・情報理工学研究科, 教授 (80158617)

Co-Investigator(Kenkyū-buntansha) KABASHIMA Yoshiyuki  Tokyo Institute of Technology, Interdisciplinary Graduate School of Science and Engineering, Associate Professor, 大学院・総合理工学研究科, 助教授 (80260652)
Project Period (FY) 2001 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2002: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2001: ¥2,000,000 (Direct Cost: ¥2,000,000)
KeywordsProbabilistic Algorithms / Randomized Algorithm / Belief Propagation / Constraint Satisfaction Problem / Low-Density Parity Check / Average-Case Analysis of Algorism / 疎行列パリティ検査符号 / Belief Propagation法 / 統計力学的手法
Research Abstract

We analyzed several randomized / probablistic algorithms for various constraint satisfaction problems.
For concrete problems, we chose (1) the decoding problem for low-density parity check codes (LDPCCD), and (2) the problem of searching a satisfying assignment of simple logical formulas (SAT). For LDPCCD, we analyzed (a) a probabilistic algorithm, so called belief propagation, and (b) a randomized local search algorithm. For both algorithms, we obtained some statistical search algorithm ; based on our analysis, we could propose an improve local search algorithm.
We also obtained some (mainly two) theoretical results on the hardness of constraint satisfaction problems in general. The first one is on the hardness of problems when we know that the solution is unique ; we gave complexity theoretic characterization to the hardness. The second one is on the average-case completeness of SAT ; we showed that complenteness notions differ when changing input distribution even sligtly.

Report

(3 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] R.Vicente, D.Saad, Y.Kabashima: "Error-Correcting Codes on a Bethe-like Lattice"Advances in Neural Information Processing Systems. 13. 322-328 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K.Nakamura, Y.Kabashima, D.Saad: "Statistical Mechanics of Low-Density Parity Check Error Correcting Codes over Galois Field"Europhysics Letters. 56. 610-616 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] D.Saad, Y.Kabashima, R.Vicent: "TAP For Parity Check Error Correcting Codes Advanced Mean Field Methods"MIT Press. 67-84 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S.Aida, R.Sculer, T.Tsukiji, O.Watanabe: "The Difference between polynominal-time many-one and truth-table reducibilities on distributional problems"Theory of Comput. Systems. 35. 449-463 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J.van Mourik, D.Saad, Y.Kabashima: "Critical Noise Levels for Low-Density Parity-Check Codes"Physical Review E. 66. 026705-1-026705-8 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y.Kabashima, K.Nakamura, J.van Mourik: "Statical Mechanics of Typical Set Decoding"Physical Review E. 66. 036125-1-036125-6 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] R. Vicente, D. Saad, and Y. Kabashima: "Error-Correcting Codes on a Bethe-like Lattice"Advances in Neural Information Processing Systems. 13. 322-328 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K. Nakamura, Y. Kabashima, and D. Saad: "Statistical Mechanics of Low-Density Party Check Error Correcting Codes over Galois Field"Europhysics Letters. 56. 610-616 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S. Aida, R. Sculer, T. Tsukiji and O. Watanabe: "The Difference between polynominal-time many-one and truth-table reducibilities on distributional problems"Theory of Comput. Systems. 35. 449-463

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J. van Mourik, D. Saad, and Y. Kabashima: "Critical Noise Levels for Low-Density Party-Check Codes"Phsyical Review E. 66. 026705-(1-8) (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y. Kabashima, K. Nakamura, and J. van Mourik: "Statical Mechanics of Typical Set Decoding"Physical Review E. 66. 036125-(1-6) (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] D. Saad, Y. Kabashima, and R. Vicent: "TAP For Parity Check Error Correcting Codes Advanced Mean Field Methods"MIT Press. 67-84 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] 澤井 健, 渡辺 治: "LDPC符号に対するランダム復号法の解析"情報処理学会,アルゴリズム研究会 SIGAL. Vol.2003. 25-32 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Aida, R., Schuler, T.Tsukiji, O.Watanabe: "The difference between polynominal-time many-one and truth-table reducibilities on distributional problems"Theory of Computing Systems. Vol.35. 449-436 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Hosaka, Y.Kabashima, H.Nishimori: "Statistical mechanics of lossy data compression using a non-monotonic perceptron"Physical Review E. 66. 066126(1)-066126(8) (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] J.van Mourik, D.Saad, Y.Kabashima: "Critical noise levels for low density parity-check codes"Physical Review E. 66. 026705(1)-026705(8) (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Kabashima, K.Nakamura, J.van Mourik: "Statistical mechanics of typical set decoding"Physical Review E. 66. 036125(1)-036125(6) (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Hofmeister, U.Schoning, R.Schuler, O.Watanabe: "A probabilistic 3-SAT Algorithm Further Improved"19th Int'l Sympos. on Theoretical Aspects of Comp.Sci. (LNCS). (掲載予定). (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Kabashima, D.Saad: "The TAP Approach to Intensive and Extensive Connectivity Systems"Advanced Mean Field Methods (MIT Press). 51-66 (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] 樺島祥介: "グラフィカルモデルと変分原理"電子情報通信学会技法. 101(616). 39-46 (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] R.Vincente, D.Saad, Y.Kabashima: "Error-correcting Codes on a Bethe-like Lattice"Advances in Neural Information Processing Systems. 13. 322-328 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] K.Nakamura, Y Kabashima, D.Saad: "Satistical Mechanics of Low-Density Party Check Error Correcting Codes over Galois Field"Europhysics Letters. 56. 610-616 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] D.Saad, Y.Kabashima, R.Vincente: "TAP For Party Chech Error Correcting Codes"Advanced Mean Field Methods (MIT Press). 67-84 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 樺島 祥介: "岩波講座 物理の世界 学習と情報の平均場理論"岩波書店. (2002)

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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