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

Analysis of Combinatorial Optimization Problems with Submodular Structures and Design of Efficient Algorithms

Research Project

Project/Area Number 01540168
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionUniversity of Tsukuba

Principal Investigator

FUJISHIGE Satoru  University of Tsukuba, Institute of Socio-Economic Planning : Professor, 社会工学系, 教授 (10092321)

Project Period (FY) 1989 – 1990
Project Status Completed (Fiscal Year 1991)
Budget Amount *help
¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1990: ¥300,000 (Direct Cost: ¥300,000)
Fiscal Year 1989: ¥700,000 (Direct Cost: ¥700,000)
KeywordsSubmodular Functions / Combinatorial Optimization / Algorithms / 離散システム / 数理計画
Research Abstract

We examined the practicality and applicability of the algorithm for the minimum norm point problem on a polytope to the submodular function minimization problem, which is a fundamental problem in combinatorial optimization problems with submodular structures. The computational experiments showed a good performance and practicality of the algorithm. However, we still have certain technical computational problem concerning the algorithm, which is left for future research. Furthermore, we proposed a concept of combinatorial hull, which is a generalization of the concept of convex hull. This gives a basis for developing a new method for solving the submodular function minimization problem in a purely combinatorial manner. We are making a progress in this direction.
Also, we developed a scaling technique for finding a maximum mean cut in a network, which is an important component in algorithms for the minimum cost flow problem. This approach can be extended to the submodular flow problem, a generalization of the minimum cost flow problem, and furnishes an efficient algorithm that is new and runs in polynomial time.
Moreover, through the two-year survey research, we examined, from the point of view of submodular and supermodular systems, the combinatorial optimization problems with submodular structures related to : base polyhedra, greedy algorithm, crossing families, generalized polymatroids, neoflows, submodular flows, independent flows, polymatroid flows, submodular analysis, submodular programs, lexicographically optimal bases, the resource allocation problem with submodular constraints etc. We gave a unifying approach to these problems and the results will be published as a monograph. Also, in the course of this survey research we found an error in the bi-truncation algorithm recently proposed by Frank and Tardos, related to the submodular function minimization problem, and showed a correct version of it.

Report

(3 results)
  • 1991 Final Research Report Summary
  • 1990 Annual Research Report
  • 1989 Annual Research Report
  • Research Products

    (13 results)

All Other

All Publications (13 results)

  • [Publications] Satoru FUJISHIGE: "A dual algorithm for finding the minimum-norm point in a polytope" Journal fo the Operations Research Society of Japan. 33. 188-195 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Takeshi MAITOH: "A note on the Frank-Tardos bi-truncation algorithm for crossing submodular functions" Mathematical Programming.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Kazuo IWANO: "A new scaling algorithm for the maximum mean cut problem" Algorithmica.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Satoru FUJISHIGE: "Submodular Functions and Optimization" North-Holland, 270 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] S. Fujishige and P. Zhan: "A dual algorithm for finding the minimum-norm point in a polytope" Journal of the Operations Research Society of Japan. 33. 188-195 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T. Naitoh and S. Fujishige: "A note on the Frank-tardos bi-truncation algorithm for crossing-submodular functions" Mathematical Programming.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] K. Iwano, S. Misono, S. Tezuka and S. Fujishige: "A new scaling algorithm for the maximum mean cut problem" Algorithmica.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] S. Fujishige: North-Holland. Submodular Functions and Optimization, 270 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Satoru FUJISHIGE: "A dual algorithm for finding the minimumーnorm point in a polytope" Journal of the Operations Research Society of Japan. 33. 188-195 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] Takeshi NAITOH: "A note on the FrankーTardos biーtruncation algorithm for crossingーsubmodular functions" Mathematical Programming.

    • Related Report
      1990 Annual Research Report
  • [Publications] Kazuo IWANO: "A new scaling algorithm for the maximum mean cut problem" Algorithmica. (to be published).

    • Related Report
      1990 Annual Research Report
  • [Publications] Satoru FUJISHIGE: "Submodular Functions and Optimization" NorthーHolland, 270 (1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] 藤重悟: "A dual algorithm for finding the minimum-norm point in a polytope" Journal of the Operations Research Society of Japan. 33. (1990)

    • Related Report
      1989 Annual Research Report

URL: 

Published: 1989-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi