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Geometric computational approach to solving hard optimization problems: theory and implementation

Research Project

Project/Area Number 24300002
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field Fundamental theory of informatics
Research InstitutionKyoto University

Principal Investigator

Avis David  京都大学, 情報学研究科, 特定教授 (90584110)

Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥15,210,000 (Direct Cost: ¥11,700,000、Indirect Cost: ¥3,510,000)
Fiscal Year 2015: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2014: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2013: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2012: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Keywords計算機科学 / 離散幾何学 / 最適化 / 幾何計算 / 大規模並列化 / 数理計画法への応用 / 多面体 / )離散最適化 / アルゴリズム / 並列処理 / 離散最適化
Outline of Final Research Achievements

The purpose of this grant was to provide funds to pursue the research goals of the Geometric Computation Laboratory (GCL) at Kyoto University, which I founded in 2010. We are concerned primarily with the ingenious use of high dimensional geometry as the driving force to provide innovative new algorithms for solving previously intractable problems of high impact in engineering and science. Typical application areas include computing Nash equilibria, PageRank optimization, supervised machine learning and mining optimization. In additional to creative new theoretical results, the laboratory will implement innovative highly parallel software to allow the results to be used in academia, industry and the society at large on problems of practical size.

Report

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

    (18 results)

All 2016 2015 2014 2013 2012 Other

All Journal Article (12 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 12 results,  Open Access: 1 results,  Acknowledgement Compliant: 4 results) Presentation (4 results) (of which Invited: 2 results) Remarks (2 results)

  • [Journal Article] On the Directed Cut Cone and Polytope2016

    • Author(s)
      David Avis and Conor Meagher
    • Journal Title

      Journal of Combinatorial Optimization

      Volume: 31 Issue: 4 Pages: 1685-1708

    • DOI

      10.1007/s10878-015-9863-0

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] A generalization of extension complexity that captures P2015

    • Author(s)
      David Avis, Hans Raj Tiwary
    • Journal Title

      Inf. Process. Lett.

      Volume: 115(6-8) Issue: 6-8 Pages: 588-593

    • DOI

      10.1016/j.ipl.2015.02.005

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] George Dantzig: father of the simplex method2015

    • Author(s)
      David Avis
    • Journal Title

      Bulletin of the EATCS

      Volume: 116 Pages: 1-2

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Ground metric learning2014

    • Author(s)
      Marco Cuturi and David Avis
    • Journal Title

      J. of Machine Learning Research

      Volume: 15 Issue: 1 Pages: 533-64

    • DOI

      10.1007/s10107-014-0764-2

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Ground metric learning2014

    • Author(s)
      Marco Cuturi and David Avis
    • Journal Title

      J. of Machine Learning Research

      Volume: 15 Pages: 533-64

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Reputation games for undirected graphs2014

    • Author(s)
      David Avis, Kazuo Iwama, Daichi Paku
    • Journal Title

      Discrete Applied Mathematics

      Volume: 166 Pages: 1-13

    • DOI

      10.1016/j.dam.2013.09.022

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Families of polytopal digraphs that do not satisfy the shelling property2013

    • Author(s)
      David Avis, Hiroyuki Miyata, Sonoko Moriyama
    • Journal Title

      Comput. Geom.

      Volume: 46(3) Issue: 3 Pages: 382-393

    • DOI

      10.1016/j.comgeo.2012.10.005

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the extension complexity of combinatorial polytopes2013

    • Author(s)
      David Avis, Hans Raj Tiwary
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 8287 Pages: 414-29

    • DOI

      10.1007/978-3-642-39206-1_6

    • ISBN
      9783642392054, 9783642392061
    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Portable Parallel Implementation of the lrs Vertex Enumeration Code2013

    • Author(s)
      David Avis, Gary Roumanis
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 8287 Pages: 414-429

    • DOI

      10.1007/978-3-319-03780-6_36

    • ISBN
      9783319037790, 9783319037806
    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Families of polytopal digraphs that do not satisfy the shelling property2013

    • Author(s)
      David Avis, Hiroyuki Miyata, Sonoko Morivama
    • Journal Title

      Computational Geometry

      Volume: 46(3) Pages: 382-393

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the extension complexity of combinatorial polytopes.2013

    • Author(s)
      David Avis, Hans Raj Tiwary
    • Journal Title

      ICALP 2013

      Volume: (Accepted)

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the existence of Hami 1 ton i ail paths for history based pivot rules on acyclic unique sink orientations of hypercubes.2012

    • Author(s)
      Yoshikazu Aoshima, David Avis, Theresa Deering, Yoshitake Mat sumo to, Sonoko Moriyama
    • Journal Title

      Discrete Applied Mathematics

      Volume: 160(15) Pages: 2104-2115

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Presentation] Markhov decision problems(MDPs), linear programming and acyclic USOs2015

    • Author(s)
      David Avis
    • Organizer
      ELC Workshop on Exponential Lower Bounds for Pivoting Algorithms
    • Place of Presentation
      CLEC, Tokyo
    • Year and Date
      2015-03-24 – 2015-03-25
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Polynomial size matching polytopes2014

    • Author(s)
      David Avis
    • Organizer
      Workshop on Extension Complexity: Update and Future Directions
    • Place of Presentation
      Kyoto University
    • Year and Date
      2014-06-09
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] On the extension complexity of combinatorial polytopes2013

    • Author(s)
      David Avis, Hans Raj Tiwary
    • Organizer
      Proc. 40th International Colloquium on Automata, Languages and Programming (ICALP 2013)
    • Place of Presentation
      Riga, Latvia
    • Related Report
      2013 Annual Research Report
  • [Presentation] A Portable Parallel Implementation of the lrs Vertex Enumeration Code2013

    • Author(s)
      David Avis, Gary Roumanis
    • Organizer
      Proc. 7th Annual International Conference on Combinatorial Optimization and Applications (COCOA 2013)
    • Place of Presentation
      Chengu, China
    • Related Report
      2013 Annual Research Report
  • [Remarks] lrs home page

    • URL

      http://cgm.cs.mcgill.ca/~avis/C/lrs.html

    • Related Report
      2015 Annual Research Report
  • [Remarks] David Avis Online publications

    • URL

      http://cgm.cs.mcgill.ca/~avis/Kyoto/

    • Related Report
      2014 Annual Research Report

URL: 

Published: 2012-04-24   Modified: 2019-07-29  

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