• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Approximation Algorithms for Submodular Optimization

Research Project

Project/Area Number 23300002
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Fundamental theory of informatics
Research InstitutionThe University of Tokyo (2012-2015)
Kyoto University (2011)

Principal Investigator

Iwata Satoru  東京大学, 情報理工学(系)研究科, 教授 (00263161)

Co-Investigator(Kenkyū-buntansha) TAKAZAWA Kenjiro  京都大学, 数理解析研究所, 助教 (10583859)
TANIGAWA Shin-ichi  京都大学, 数理解析研究所, 助教 (30623540)
Project Period (FY) 2011-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥12,610,000 (Direct Cost: ¥9,700,000、Indirect Cost: ¥2,910,000)
Fiscal Year 2014: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2013: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2012: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2011: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Keywords離散最適化 / 劣モジュラ関数 / 近似アルゴリズム / NP困難 / ネットワーク / 離散凸性 / 巡回セールスマン問題 / 組合せ剛性理論
Outline of Final Research Achievements

Submodularity is known to be a common structure among various efficiently solvable discrete optimization problems. On the other hand, most discrete optimization problems that arise in practice are NP-hard, and researchers have designed efficient algorithms for finding approximately optimal solutions. Combining these two streams of research in discrete optimization, we have tried to develop a systematic approach to design approximation algorithms for a generic framework of submodular optimization. In particular, we have provided a 1/2-approximation algorithm for maximizing k-submodular functions. We have also designed an approximation algorithm for maximizing monotone k-submodular functions within the ratio of k/2(k-1).

Report

(5 results)
  • 2015 Final Research Report ( PDF )
  • 2014 Annual Research Report
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • Research Products

    (22 results)

All 2016 2015 2014 2013 2012 2011 Other

All Journal Article (9 results) (of which Peer Reviewed: 8 results,  Acknowledgement Compliant: 3 results,  Open Access: 1 results) Presentation (10 results) (of which Int'l Joint Research: 1 results,  Invited: 2 results) Remarks (3 results)

  • [Journal Article] Improved Approximation Algorithms for k-Submodular Function Maximization2016

    • Author(s)
      Satoru Iwata, Shin-ichi Tanigawa, and Yuichi Yoshida
    • Journal Title

      Proceedings of the 27th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)

      Volume: なし Pages: 404-413

    • DOI

      10.1137/1.9781611974331.ch30

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Finding a stable allocation in polymatroid intersection2016

    • Author(s)
      S. Iwata and Y. Yokoi
    • Journal Title

      Proceedings of the 27th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2016)

      Volume: - Pages: 1034-1047

    • DOI

      10.1137/1.9781611974331.ch73

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Testing Supermodular-cut Condition2015

    • Author(s)
      Shin-ichi Tanigawa and Yuichi Yoshida
    • Journal Title

      Algorithmica

      Volume: 71 Issue: 4 Pages: 1065-1075

    • DOI

      10.1007/s00453-013-9842-8

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Orientations and detachments of graphs with prescribed degrees and connectivity2014

    • Author(s)
      Satoru Iwata and Tibor Jordan
    • Journal Title

      Discrete Optimization

      Volume: 12 Pages: 121-128

    • DOI

      10.1016/j.disopt.2014.02.003

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Optimal matching forests and valuated delta-matroids,2014

    • Author(s)
      Kenjiro Takazawa
    • Journal Title

      SIAM Journal on Discrete Mathematics

      Volume: 28 Issue: 1 Pages: 445-467

    • DOI

      10.1137/110827661

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Combinatorial conditions for the unique completability of low rank matrices2014

    • Author(s)
      Bill Jackson, Tibor Jordan, and Shin-ichi Tanigawa
    • Journal Title

      SIAM Journal on Discrete Mathematics

      Volume: 28 Issue: 4 Pages: 1797-1819

    • DOI

      10.1137/140960098

    • NAID

      120005549943

    • Related Report
      2013 Annual Research Report
  • [Journal Article] Approximating max-min weighted T-joins2013

    • Author(s)
      S. Iwata and R. Ravi
    • Journal Title

      Operations Research Letters

      Volume: Vol.41 Issue: 4 Pages: 321-324

    • DOI

      10.1016/j.orl.2013.03.004

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Finding 2-Factors Closer to TSP Tours in Cubic Graphs2013

    • Author(s)
      S. Boyd, S. Iwata, and K. Takazawa
    • Journal Title

      SIAM Journal on Discrete Mathematics

      Volume: 27 Issue: 2 Pages: 918-939

    • DOI

      10.1137/110841837

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A flow model based onpolylinking systems2012

    • Author(s)
      M .X .Goemans, S .Iwata, and R .Zenklusen
    • Journal Title

      Mathematical Programming

      Volume: Vol.135 Issue: 1-2 Pages: 1-23

    • DOI

      10.1007/s10107-011-0446-2

    • Related Report
      2012 Annual Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Presentation] Finding a Stable Allocation in Polymatroid Intersection2015

    • Author(s)
      Satoru Iwata and Yu Yokoi
    • Organizer
      The 22th International Symposium on Mathematical Programming
    • Place of Presentation
      Pittsburgh, USA
    • Year and Date
      2015-07-12
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Graph-TSP from Steiner Cycles2014

    • Author(s)
      Satoru Iwata, Alantha Newman, and R. Ravi
    • Organizer
      40th International Workshop on Graph-Theoretic Concepts in Computer Science
    • Place of Presentation
      Orleans, フランス
    • Year and Date
      2014-06-25 – 2014-06-27
    • Related Report
      2013 Annual Research Report
  • [Presentation] Conditions for the Unique Completability of Low Rank Positive Semidefinite Matrices2014

    • Author(s)
      Shin-ichi Tanigawa
    • Organizer
      Japanese-Swiss Workshop on Combinatorics and Computational Geometry
    • Place of Presentation
      東京大学, 東京
    • Year and Date
      2014-06-04 – 2014-06-06
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Conditions for the Unique Completability of Low Rank Positive Semidefinite Matrices2014

    • Author(s)
      Shin-ichi Tanigawa
    • Organizer
      Japan Conference on Graph Theory and Combinatorics
    • Place of Presentation
      日本大学, 東京
    • Year and Date
      2014-05-17 – 2014-05-21
    • Related Report
      2013 Annual Research Report
  • [Presentation] Finding 2-Factors Closer to TSP Tours in Cubic Graphs2014

    • Author(s)
      Kenjiro Takazawa
    • Organizer
      The 18th Aussois Combinatorial Optimization Workshop
    • Place of Presentation
      Aussois, フランス
    • Year and Date
      2014-01-06 – 2014-01-10
    • Related Report
      2013 Annual Research Report
  • [Presentation] Submodular Functions: Minimization and Approximation Algorithms2013

    • Author(s)
      Satoru Iwata, Alantha Newman, and R. Ravi
    • Organizer
      Fourth Cargese Workshop on Combinatorial Optimization
    • Place of Presentation
      Cargese, フランス
    • Year and Date
      2013-09-30 – 2013-10-05
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Shortest Bibranchings and Valuated Matroid Intersection2013

    • Author(s)
      Kenjiro Takazawa
    • Organizer
      Combinatorial Geometries: Matroids, Oriented Matroids and Applications
    • Place of Presentation
      Marseille, フランス
    • Year and Date
      2013-04-02 – 2013-04-06
    • Related Report
      2013 Annual Research Report
  • [Presentation] Minimum Linear Ordering with Submodular/Supermodular Functions2012

    • Author(s)
      S.Iwata, P.Tetali, P.Tripathi
    • Organizer
      Modern Aspects of Submodularity
    • Place of Presentation
      Georgia工科大学(USA)(招待講演)
    • Year and Date
      2012-03-22
    • Related Report
      2011 Annual Research Report
  • [Presentation] Approximating Minimum Linear Ordering Problems2012

    • Author(s)
      S. Iwata, P. Tetali, and P. Tripathi
    • Organizer
      The 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems
    • Place of Presentation
      Boston (アメリカ合衆国)
    • Related Report
      2012 Annual Research Report
  • [Presentation] Submodular Optimization and Approximation Algorithms2011

    • Author(s)
      S.Iwata
    • Organizer
      The Fifth Sino-Japanese Optimization Meeting
    • Place of Presentation
      中国科学院北京(中国)(招待講演)
    • Year and Date
      2011-09-28
    • Related Report
      2011 Annual Research Report
  • [Remarks]

    • URL

      http://www.opt.mist.i.u-tokyo.ac.jp/~iwata

    • Related Report
      2014 Annual Research Report
  • [Remarks] http://www.opt.mist.i.u-tokyo.ac.jp/~iwata

    • Related Report
      2013 Annual Research Report
  • [Remarks] Satoru Iwata

    • URL

      http://www.opt.mist.i.u-tokyo.ac.jp/~iwata

    • Related Report
      2012 Annual Research Report

URL: 

Published: 2011-04-06   Modified: 2019-07-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi