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A Study of Approximation Algorithms for Graph Problems

Research Project

Project/Area Number 21500011
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Fundamental theory of informatics
Research InstitutionNagoya University

Principal Investigator

HIRATA Tomio  名古屋大学, 情報科学研究科, 教授 (10144205)

Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordsアルゴリズム理論 / 近似アルゴリズム / アルゴリズム / 近似困難性 / 2部クリーク / 2部クリーク被覆 / 2部クリーク分割 / 2クリーク分割 / 独立集合
Research Abstract

The purpose of this research is the design and analysis of approximation algorithms for the independent problem and the biclique covering(partitioning) problem of a graph. For the independent set problem, we proposed a notion of“weighted degree"of a vertex in a weighted graph, and gave approximation algorithms. We also gave an approximation algorithm for finding an independent set of a C_k-free graph. For the biclique covering problem, we proposed a method using a“set covering approach,"and for the biclique partition problem, we gave a formulation using the“exclusive rank"of a Boolean matrix. Furthermore, we discussed the approximation hardness of this problem.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (18 results)

All 2012 2011 2010 2009 Other

All Journal Article (15 results) (of which Peer Reviewed: 10 results) Presentation (3 results)

  • [Journal Article] 距離遺伝2部グラフ上のハミルトン閉路アルゴリズム2012

    • Author(s)
      高須賀将秀、平田富夫
    • Journal Title

      京都大学数理解析研究所講究禄

      Volume: (印刷中)

    • Related Report
      2011 Annual Research Report
  • [Journal Article] たて糸張力均一条件下における綜絖枠数最小化2011

    • Author(s)
      松浦勇, 平田富夫
    • Journal Title

      電子情報通信学会コンピュテーション研究会技術報告

      Volume: 43 Pages: 53-60

    • NAID

      10031108838

    • Related Report
      2011 Final Research Report
  • [Journal Article] たて糸張力均一条件下における綜絖枠数最小化2011

    • Author(s)
      松浦勇、平田富夫
    • Journal Title

      電子情報通信学会コンピュテーション研究会技術報告

      Volume: COMP2011-43 Pages: 53-60

    • NAID

      10031108838

    • Related Report
      2011 Annual Research Report
  • [Journal Article] A new bound for the approximation ratio of the minimum biclique edge partition problem2010

    • Author(s)
      H. Otsuki, T. Hirata
    • Journal Title

      Proceedings of CGGA, Dailian

      Pages: 96-97

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Inapproxi mability of the minimum biclique edge partition problem2010

    • Author(s)
      H. Otsuki, T. Hirata
    • Journal Title

      IEICE Transactions of Information & Systems

      Volume: Vol.E93-D Pages: 290-292

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] 集合基底問題の正規基底を求めるヒューリスティックアルゴリズム2010

    • Author(s)
      大月英明, 平田富夫
    • Journal Title

      情報処理学会アルゴリズム研究会資料

      Volume: AL-128 Pages: 1-10

    • NAID

      110007995603

    • Related Report
      2011 Final Research Report
  • [Journal Article] Inapproximability of the minimum biclique edge partition problem2010

    • Author(s)
      H.Ootsuki, T.Hirata
    • Journal Title

      IEICE TRANSACTIONS on Foundations of Computer Science E93-D

      Pages: 290-292

    • NAID

      10026813643

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A textile design and the Boolean rank problem2009

    • Author(s)
      I. Matsuura, M. Yagiura, T. Hirata
    • Journal Title

      IADIS International Conference on Applied Computing

      Pages: 345-352

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] ドビー織機の綜絖枠数最小化問題に対する集合被覆アプローチ2009

    • Author(s)
      松浦勇, 柳浦睦憲, 平田富夫
    • Journal Title

      情報処理学会論文誌

      Volume: Vol.50, No.6 Pages: 1539-1548

    • NAID

      40019550713

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A note on the greedy algorithm for finding independent sets of C_k-free graphs2009

    • Author(s)
      I. Koura, T. Ono, T. Hirata
    • Journal Title

      Information Processing Letters

      Volume: Vol.109 Pages: 485-489

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Approximation algorithms for the weighted independent set problem in sparse graphs2009

    • Author(s)
      A. Kako, T. Ono, T. Hirata M. M. Halldorsson
    • Journal Title

      Discrete Applied Mathematics

      Volume: Vol.157 Pages: 617-626

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Approximation algorithms for the weighted independent set problem in sparse graphs2009

    • Author(s)
      A.Kako, T.Ono, T.Hirata, M.M.Halldorsson
    • Journal Title

      Discrete Applied Mathematics 57

      Pages: 617-626

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A note on the greedy algorithm for finding independent sets of C -k-freegraphs2009

    • Author(s)
      I.Koura, T.Ono, T.Hirata
    • Journal Title

      Information Processing Letters 109

      Pages: 485-489

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] ドビー織機の綜絖枠数最小化問題に対する集合被覆アプローチ2009

    • Author(s)
      松浦勇、柳浦睦憲、平田富夫
    • Journal Title

      情報処理学会論文誌 50

      Pages: 1539-1548

    • NAID

      40019550713

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 距離遺伝2部グラフ上のハミルトン閉路アルゴリズム

    • Author(s)
      高須賀将秀, 平田富夫
    • Journal Title

      京都大学数理解析研究所講究禄

    • Related Report
      2011 Final Research Report
  • [Presentation] A new bound for the approximation ratio of the minimum biclique edge partition problem2010

    • Author(s)
      H.Otsuki, T.Hirata
    • Organizer
      The China-Japan Join Conference on Computer Geometry, Graphs and Applications
    • Place of Presentation
      大連(中国)
    • Year and Date
      2010-11-04
    • Related Report
      2010 Annual Research Report
  • [Presentation] 集合基底問題の正規基底を求めるヒューリスティックアルゴリズム2010

    • Author(s)
      大月英明、平田富夫
    • Organizer
      情報処理学会アルゴリズム研究会
    • Place of Presentation
      九州大学
    • Year and Date
      2010-01-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] A textile design and the Boolean rank problem2009

    • Author(s)
      Tomio Hirata
    • Organizer
      IADIS International Conference Applied Computing 2009
    • Place of Presentation
      Rome
    • Year and Date
      2009-11-20
    • Related Report
      2009 Annual Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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