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On Construction and Evaluation of Parallel and Randomized Algorithms for Network Optimization Problems

Research Project

Project/Area Number 05680281
Research Category

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

Allocation TypeSingle-year Grants
Research Field 計算機科学
Research InstitutionKOBE UNIVERSITY OF COMMERCE

Principal Investigator

KATOH Naoki  Kobe University of commerce, Dept.Management Science, Professor, 商経学部, 教授 (40145826)

Co-Investigator(Kenkyū-buntansha) DAI Yang  Kobe University of commerce, Dept.Management Science, Research Assistant, 商経学部, 助手 (40244678)
Project Period (FY) 1993 – 1994
Project Status Completed (Fiscal Year 1994)
Budget Amount *help
¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 1994: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1993: ¥1,100,000 (Direct Cost: ¥1,100,000)
Keywordsnetwork optimization / minimum range cut / minimum cut / randomized algorithm / parallel algorithm / color quantization / minimum k-clustering / 最小κ-クラスタリング / 最小k-カット / 最大格差最小k-カット / 確率的近似アルゴリズム / 回路分割
Research Abstract

Over the last two years, we have tried to construct new parallel, randomized algorithms for network optimization problems, in particular for minimum cut problems. Recently, there has been much progress in the research of parallel and randomized algorithms for minimum cut problems. In this research project, we have focused on developing simple and efficient algorithms that work for a broader class of problems including minimum cut problems. In addition, we have also studied minimum k-clustering problems and could achieve new theoretical results on the problem under minimum variance criterion.
In this project, we have first developed an O (m+nlogn) time algorithm for minimum range cut problems (n and m are the numbers of nodes and vertices in a graph). A minimum range cut problems asks to find a cut in weighted undirected graphs that minimizes the difference between maximum and minimum edge weights in the cut. Based on this algorithm, we developed a parallel, randomized algorithm for minimum cut problems. We then carried out extensive computer experiments to demonstrate the effectiveness of our approximate algorithm. As a result, we could show that our algorithm computes cuts that are very close to exact ones in time much faster than existing exact algorithms. We have further extended this algorithm to minimum k-cut problems and performed similar experiments.
A minimum k-clustering problem asks to find a k-partition of a given set of n points in R^d based on certain optimality criteria. In our study, focusing on the application to color quantization problems arising in computer graphics, we have proposed randomized algorithms to find optimal k-partition under certain optimality criteria that are suitable for this application.

Report

(3 results)
  • 1994 Annual Research Report   Final Research Report Summary
  • 1993 Annual Research Report
  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] D.de Werra,P.Hell,T.Kameda,N.Katoh,Ph.Solot,M.Yamashita: "Graph Endpoint Coloring and Distributed Processing" Networks. 23. 93-98 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] S.Hasegawa,H.Imai,M.Inaba,N.Katoh,J.Nakano: "Efficient Algorithms for Variance-based k-clustering" Proceedings of the First Pacific Conference on Computer Graphics and Applications. 75-89 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Y.Dai,H.Imai,K.Iwano,N.Katoh: "How to Delete Requests in Semi-Online Problems" Proceedings of 4th International Symposium of Algorithms and Computation,ISAAC'93. 48-57 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] 戴陽,岩野和生,加藤直樹: "最大格差最小k-カットアルゴリズムによる最小カットk-カット問題の近似解法" 電気学会論文誌C. 114. 438-443 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] M.Inaba,N.Katoh,H.Imai: "Applications of Weighted Voronoi Diagrams and Randomization to Variance-Based k-Clustering" Proc.of ACM 10th Symposium on Computational Geometry. 332-339 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Y.Dai,H.Imai,K.Iwano,N.Katoh,K.Ohtsuka,N.Yoshimura: "A new unifying heuristic algorithm for unidrected minimum cut problems using minimum range cut algorithms" Discrete Applied Mathematics. 発表予定.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] D.de Werra, P.Hell, T.Kameda, N.Katoh, Ph.Solot and M.Yamashita: "Graph Endpoint Coloring and Distributed Processing" Networks. Vol.23No.2. 93-98 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] S.Hasegawa, H.Imai, M.Inaba, N.Katoh and J.Nakano: "Efficient Algorithms for Variance-based k-clustering" Proceedings of the First Pacific Conference on Computer Graphics and Applications. 75-89 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Y.Dai, H.Imai, K.Iwano and N.Katoh: "How to Delete Requests in Semi-Online Problems" Proceedings of 4th International Symposium of Algorithms and Computation, ISAAC'93. 48-57 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Y.Dai, K.Iwano, N.Katoh: "A new approximate algorithm for minimum k-cut problem by using minimum range k-cut algorithm (in Japanese)" Publication of Electronics, Information and System Society of Japan. Vol.114, No.4. 438-443 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] M.Inaba, N.Katoh and H.Imai: "Applications of Weighted Voronoi Diagrams and Randomization to Variance-Based k-Clustering" Proceedings of ACM 10th Symposium on Computational Geometry. 332-339 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Y.Dai, H.Imai, K.Iwano, N.Katoh, K.Ohtsuka and N.Yoshimura: "A new unifying heuristic algorithm for the unidrected minimum cut problems using minimum range cut algorithms" Discrete Applied Mathematics. (to appear.).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] D.de Werra,P.Hell,T.Kameda,N.Katoh,Ph.Solot,M.Yamashita: "Graph Endpoint Coloring and Distributed Processing" Networks. 23. 93-98 (1993)

    • Related Report
      1994 Annual Research Report
  • [Publications] S.Hasegawa,H.Imai,M.Inaba,N.Katoh,J.Nakano: "Efficient Algorithms for Variance-based κ-clustering." Proceedings of the First Pacific Conference on Computer Graphics and Applications. 75-89 (1993)

    • Related Report
      1994 Annual Research Report
  • [Publications] Y.Dai,H.Imai,K.Iwano,N.Katoh: "How to Delete Requests in Semi-Online Problems" Proceedings of 4th International Symposium of Algorithms and Computation,ISAAC'93. 48-57 (1993)

    • Related Report
      1994 Annual Research Report
  • [Publications] 戴陽,岩野和生,加藤直樹: "最大格差最小k-カットアルゴリズムによる最小κ-カット問題の近似解法" 電気学会論文誌C. 114. 438-443 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] M.Inaba,N.Katoh,H.Imai: "Applications of Weighted Voronoi Diagrams and Randomization to Variance-Based κ-Clustering" Proc.of ACM 10th Symposium on Computational Geometry. 332-339 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Y.Dai,H.Imai,K.Iwano,N.Katoh,K.Ohtsuka,N.Yoshimura: "A new unifying heuristic algorithm for the umidrected minimum cut problems using minimum range cut algorithms" Discrete Applied Mathematics. (発表予定).

    • Related Report
      1994 Annual Research Report
  • [Publications] Yang DAI(その他 3名): "How to treat delete requests in semi-online problems" Algorithms and Computation.Proc,of 4th ISAAC,Lecture Notes in Computer Science. 762. 48-57 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Yang DAI(その他 2名): "最大格差最小k-カットアルゴリズムによる最小k-カット問題の近似解法" 電気学会部門誌(C). (発表予定). (1994)

    • Related Report
      1993 Annual Research Report
  • [Publications] Kazuo IWANO(その他 1名): "Efficient Algorithm for finding the most vital edge of a minimum spanning tree" Information Processing Letters. 48. 211-213 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Susumu HASEGAWA(その他 4名): "Efficient Algorithms for variance-baseil k-clustering" Computer Graphics and Applications,Proc,of 1st pacific Conference on Computer Graphics and Applications-Pacific Graphics ′93. 1. 75-89 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Yang DAI(その他 1名): "Linear stationary point problems on Unbcunded polyhedra" Mathematics of Operations Research. 18. 635-644 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Yang DAI(その他 1名): "A continuous deformation algorithm for variational inequality problems on polytope" Mathematical Progremming. (発表予定). (1994)

    • Related Report
      1993 Annual Research Report

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Published: 1993-04-01   Modified: 2016-04-21  

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