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A Study of Approximation Algorithms for Combinatorial Optimization Problems

Research Project

Project/Area Number 10680350
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

HIRATA Tomio  School of Engineering, Nagoya University, Professor, 工学研究科, 教授 (10144205)

Co-Investigator(Kenkyū-buntansha) ISO Naoyuki  Chuko University, Associate Professor, 情報科学部, 講師 (80283406)
ONO Takao  School of Engineering, Nagoya University, Assistant Professor, 工学研究科, 助手 (60311718)
FUJITO Toshihiro  School of Engineering, Nagoya University, Associate Professor, 工学研究科, 助教授 (00271073)
Project Period (FY) 1998 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 2000: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1999: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1998: ¥1,300,000 (Direct Cost: ¥1,300,000)
Keywordsapproximation algorithm / satisfiability problem / max cut / edge dominating set / layout design / logic emulator / 距離変換 / ネット割り当て問題 / 辺支配集合問題 / ペトリネット / 頂点除去問題 / マトロイド / 充足最大化問題 / 判定値計画法 / 摂動
Research Abstract

The purpose of this research is to develop efficient approximation algorithms with high performance ratio for various combinatorial optimization problems. The problems we treat includes the satisfiability of a Boolean expression (MAX SAT), the maximum cut of a graph (MAX CUT) and the edge-dominating set of a graph. Since these problems are all NP-hard, it is theoretically, as well as practically, important to develop approximation algorithms with high performance ratio.
The results obtained are as follows. We introduced perturbation on a truth assignment and obtained a better algorithm for MAX SAT.We proposed an algorithm for the minimization of vias in the VLSI layout design. We designed an efficient algorithm for the Euclidean distance transform and gave an uniform method for morphology operations in picture processing. We designed an efficient algorithm for the net assignment problem in logic emulator, which is used for logic verification process in designing large scale circuits. Furthermore, approximability of the edge dominating set problem and its related ones are also investigated.

Report

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

    (25 results)

All Other

All Publications (25 results)

  • [Publications] Ono,T.,Hirata,T.: ""An Improved Algorithm for the Net Assignment Problem""IEICE on Fundamentals. Vol.E84-A No.5. (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Hirata,T.,Ono,T. :: ""Approximation Algorithms for MAX SAT""IEICE on Fundamentals,. Vol.E83-D No.3. 488-495 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 櫻井敦史,平田富夫: ""効率の良いモルフォロジー演算が可能なフィルタ形状について""情報処理学会論文誌. Vol.41 No.12. 3344-3351 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 磯直行,平田富夫: ""平面配線可能性検証アルゴリズムの実現""情報処理学会論文誌. Vol.40 No.4. 1636-1643 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 小野孝男,平田富夫,浅野孝夫: ""摂動法によるMAX SAT近似アルゴリズムの改良""電子情報通信学会論文誌. Vol.J81-D-I No.9. 1107-1111 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Fujito,T.: ""Approximation Algorithms for Submodular Set Cover with Applications""IEICE Trans.Inf. & Syst.. Vol.E83-D,No.3,. 170-177 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Ono, T.Hirata: "An Improved Algorithm for the Net Assignment Problem"IEICE Trans.on Fundamentals. Vol.E84-A, No.5(to appear). (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Hirata, T.Ono: "Approximation Algorithms for MAX SAT"IEICE Trans.on Fundamentals. Vol.E83-D, No.3. 488-495 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] A.Sakurai, T.Hirata: "On a Class of Efficiently Computable Morphological filters"Trans.IPSJ. Vol.41, No.12. 3344-3351 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] N.ISO, T.Hirata: "Implementation of Routability Checking Algorithm for Planar Layouts"Trans.IPSJ. Vol.40, No.4. 1636-1643 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Ono, T.Hirata, T.Asano: "Improvement of MAX SAT Approximation Algorithm with Perturbation"Trans.of IEICE. Vol.J81-D-I, No.9(in Japanese). 1107-1111 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Fujito: "Approximation Algorithms for Submodular Set Cover with Applications"IEICE Trans.on Inf.& Syst.. Vol.E83-D, No.3. 170-177 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Ono,T.,Hirata,T.: ""An Improved Algorithm for the Net Assignment Problem","IEICE on Fundamentals, Vol.E84-A,No.5,2001.. Vol E84-A No.3. (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] Hirata,T.,Ono,T.: ""Approximation Algorithms for MAX SAT"" IEICE on Fundamentals.Vol.E83-D,No.3,pp.488-495,2000.. Vol.E83-D No.3. 488-495 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 櫻井敦史,平田富夫: ""効率の良いモルフォロジー演算が可能なフィルタ形状について""情報処理学会論文誌. Vol.41,No.12. 3344-3351 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Fujito,T.:: ""Approximation Algorithms for Submodular Set Cover with Applications""IEICE Trans.Inf.& Syst.. Vol.E83-D No.3. 170-177 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Fujito,T.,Taoka,S.Watanabe,T.: ""On the Legal Firing Sequence Problem of Petri Nets with Cactus Structure" "ICE Trans.Fundamentals. Vol.E83-A No.3. 124-131 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Fujito,T.:: ""Approximating Minimum Feedback Vertex Sets in Hypergraphs""Theoretical Computer Science. Vol.246. 107-116 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Toshihiro Fujito: "Approximating Node-Deletion Problems for Matroidal Properties"Journal of Algorithms. Vol.31 No.1. 211-227 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Toshihiro Fujito: "On Approximation of the Submodular Set Cover Problem"Operations Reseach Letters. Vol.25 No.4. 169-174 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 櫻井敦史: "効率の良いモルフォロジー演算が可能なフィルタ形状について"電子情報通信学会 技術研究報告書. COMP 99 No.56. 1-8 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 宮田優治: "2層配線における発見的ビア数最小化手法"電子情報通信学会 技術研究報告書. (発行予定). (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] 磯 直行: "平面配線可能性検証アルゴリズムの実現" 情報処理学会論文誌. Vol.40 No.4(未定). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] Toshihiro Fujito: "A Unified Approximation Algorithm for Node-Delection Problems" Discrete Applied Mathematics. Vol.86. 213-231 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Toshihiro Fujito: "Approximating Node-Deletion Problems for Matroidal Properties" Journal of Algorithms. 未定.

    • Related Report
      1998 Annual Research Report

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Published: 1998-04-01   Modified: 2016-04-21  

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