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Development of algorithms for solving graph/network problems

Research Project

Project/Area Number 10205213
Research Category

Grant-in-Aid for Scientific Research on Priority Areas (B)

Allocation TypeSingle-year Grants
Research InstitutionToyohashi University of Technology (TUT) (2000-2001)
Kyoto University (1998-1999)

Principal Investigator

NAGAMOCHI Hiroshi  Toyohashi University of Technology, Dept. Information and Computer Sciences, Professor, 工学部, 教授 (70202231)

Co-Investigator(Kenkyū-buntansha) ISHII Toshimasa  Toyohashi University of Technology, Dept. Information and Computer Sciences, Assistant Professor, 工学部, 助手 (30324487)
Project Period (FY) 1998 – 2000
Project Status Completed (Fiscal Year 2001)
Budget Amount *help
¥10,000,000 (Direct Cost: ¥10,000,000)
Fiscal Year 2000: ¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 1999: ¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 1998: ¥4,400,000 (Direct Cost: ¥4,400,000)
Keywordsgraph algorithm / minimum cut / connectivity / combinatorial optimization / combinatorial optimization game / graph partition / approximation algorithm / connectivity augmentation / 離散最適化 / ネットワーク問題 / 最小カット問題 / 協力ゲーム / グラフ連結度 / 劣モジュール関数 / アルゴリズム / グラフ・ネットワーク / 最適化 / 劣モジュラ関数
Research Abstract

In this research, we have developed efficient graph algorithms and clarified graph structures in the graph/network problems.
We have obtained the following results for the problems related to connectivity. We have improved the time complexity for representing all minimum cuts in a cactus. To achieve this, we used a maximum adjacency ordering, a graph search procedure by which all minimum cuts can be found without using the maximum-flow algorithm. A subset of edges is called a k-cut if removal of it results in k components. We have reduced the time bound for computing a minimum k-cut for k=3,4,5,6 by a new approach that enumerates 2-cut in the nondecreasing order of weights. We have proved that necessary information to solve the k-edge-connectivity augmentation problem can be extracted from an appropriate set of cuts with size less than k in a given graph. By using such a set of cuts, we can control structure of solutions to the edge-connectivity augmentation problem.
We have also obtained the following results in designing approximation algorithms. For the vertex-connectivity problem with a target value k, an approximation algorithm was proposed only for the case where a given graph is (k-1)-vertex-connected. We extend the algorithm so that it works for an arbitrary input graph. Our algorithm delivers an solution with absolute error 2(α-k)k, where α =the vertex-connectivity of an input graph. We have studied the problem of increasing the edge- and vertex-connectivities at the same time, and gave an approximation algorithm with absolute error that depends only on the target values. We have also designed a (7/2)-approximation algorithm for the weighted 3-vertex-connectivity augmentation problem, a 2-approximation algorithm for the weighted minimum edge dominating set problem and a dH(r)-approximation algorithm for the network design problem in hypergraph with degree d, where r is the maximum demand and H() is the harmonic function.

Report

(4 results)
  • 2001 Final Research Report Summary
  • 2000 Annual Research Report
  • 1999 Annual Research Report
  • 1998 Annual Research Report
  • Research Products

    (176 results)

All Other

All Publications (176 results)

  • [Publications] 永持 仁: "初等的フローゲームの凸性について"電子情報通信学会論文誌. J81-D-I. 666-676 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A.Frank: "Two arc-disjoint paths in Eulerian digraphs"SIAM J.Disc.Math.. vol.11,no.4. 557-589 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Ibaraki: "A fast algorithm for finding a maximum free multiflow in an inner Eulerian network and some generalizations"Combinatorica. vol.18,no.1. 61-93 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "A note on minimizing submodular functions"Information Processing Letters. vol.67. 239-244 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Ishii: "Optimal augmentation of a biconnected graph to a k-edge-connected and triconnected graph"Proceedings 9th Annual ACM-SIAM Symposium on Discrete Algorithms. 280-289 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Hasunuma: "Independent spanning trees with small depths in iterated line digraphs"Australian Computer Science Communications. vol.20,no.3. 21-35 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "Edge-splitting and edge-connectivity augmentation in planar graphs"Lecture Notes in Computer Science. vol.1412. 96-111 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Y.Karuno: "A 1.5-approximation for single-vehicle scheduling problem on a line with release and handling times"Japan-U.S.A.Symposium on Flexible Automation. 1363-1366 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Ishii: "k-edge and 3-vertex connectivity augmentation in an arbitrary multigraph"Lecture Notes in Computer Science. vol.1533. 159-168 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "Polyhedral structure of submodular and posi-modular systems"Lecture Notes in Computer Science. vol.1533. 169-178 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "An efficient NC algorithm for a sparse k-edge-connectivity certificate"Lecture Notes in Computer Science. vol.1533. 447-456 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "Augmenting edge-connectivity over the entire range in O(nm)time"J.Algorithms. vol.30. 253-301 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "Augmenting a submodular and posi-modular set function by a multigraph"Proceedings of the 1st Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications. 237-279 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "A fast algorithm for computing minimum 3-way and 4-way cuts"Lecture Notes in Computer Science. vol.1610. 377-390 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Ishii: "Augmenting an (l-1)-vertex-connected multigraph to a k-edge-connected and l-vertex-connected multigraph"Lecture Notes in Computer Science. vol.1643. 414-425 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "An approximation for finding a smallest 2-edge-connected subgraph containing a specified spanning tree"Lecture Notes in Computer Science. vol.1627. 31-40 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "A faster algorithm for computing minimum 5-way and 6-way cuts in graphs"Lecture Notes in Computer Science. vol.1627. 164-173 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "Bisecting two subsets in 3-connected graphs"Lecture Notes in Computer Science. vol.1741. 425-434 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] L.Zhao: "Approximating the minimum k-way cut in a graph via minimum 3-way cuts"Lecture Notes in Computer Science. vol.1741. 373-382 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "An approximation of the minimum vertex cover in a graph"J.of Japan Society for Industrial and Applied Mathematics. vol.16,no.3. 369-375 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] X.Deng: "Algorithmic aspects of the core of combinatorial optimization games"Math.of Operations Research. vol.24,no.3. 751-766 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "A simple proof of a minimum cut algorithm and its applications"Inst.Electron.Inform.Comm.Eng.Trans.Fundamentals. vol.E82-A,no.10. 2231-2236 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] P.Eades: "Drawing clustered graphs on an orthogonal grid"Journal of Graph Algorithms and Application. vol.3,no.4. 3-29 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "A simplified O(nm)time edge-splitting algorithm in undirected graphs"Algorithmica. vol.26. 56-67 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "Recent development of graph connectivity augmentation algorithms"Inst.Electron.Inform.Comm.Eng.Trans.Fundamentals. vol.E83-D,no.3. 372-383 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Ishii: "Optimal augmentation of a 2-vertex-connected multigraph to a k-edge-connected and 3-vertex-connected multigraph"J.Combinatorial Optimization. vol.4. 35-78 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "A fast algorithm for cactus representations of minimum cuts"J.of Japan Society for Industrial and Applied Mathematics. vol.17,no.2. 245-264 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "A faster algorithm for computing minimum 5-way and 6-way cuts in graphs"J.Combinatorial Optimization. vol.4. 151-169 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "A 7/3-approximation for the minimum weight 3-connected spanning subgraph problem"Inst.Electron.Inform.Comm.Eng.Trans.Fundamentals. vol.E83-A,no.4. 687-691 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "A fast algorithm for computing minimum 3-way and 4-way cuts"Mathematical Programming. vol.88,no.3. 507-520 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] X.Deng: "Totally balanced combinatorial optimization games"Mathematical Programming. vol.87. 441-452 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "Polyhedral structure of submodular and posi-modular systems"Discrete Applied Mathematics. vol.107. 165-189 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Ishii: "On the minimum augmentation of an 1-connected graph to a k-connected graph"Lecture Notes in Computer Science. vol.1851. 286-299 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Ishii: "Simultaneous augmentation of two graphs to an 1-edge-connected graph and a biconnected graph"Lecture Notes in Computer Science. vol.1969. 326-337 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] L.Zhao: "A primal-dual approximation algorithm for the survivable network design problem in hypergraphs"Lecture Notes in Computer Science. vol.2010. 478-489 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Y.Karuno: "A 2-approximation algorithm for the multi-vehicle scheduling on a path with release and handling times"Lecture Notes in Computer Science. vol.2161. 218-229 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Y.Karuno: "A polynomial time approximation scheme for the multi-vehicle scheduling on a path with release and handling times"Lecture Notes in Computer Science. vol.2223. 36-47 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "On the minimum local-vertex-connectivity augmentation in graphs"Lecture Notes in Computer Science. vol.2223. 124-135 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] L.Zhao: "A unified framework for approximating some partition problems via greedy splitting"Lecture Notes in Computer Science. vol.2223. 682-694 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "Augmenting a submodular and posi-modular set function by a multigraph"J.Combinatorial Optimization. vol.5,no.2. 175-212 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "An efficient NC algorithm for a sparse k-edge-connectivity certificate"J.Algorithms. vol.38,no.2. 354-373 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "Solving the single-vehicle scheduling problem for all home locations under depth-first routing on a tree"Inst.Electron.Inform.Comm.Eng.Trans.Fundamentals. vol.E84-A,no.5. 1135-1143 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Ishii: "Multigraph augmentation under biconnectivity and general edge-connectivity requirements"Networks. vol.37,no.3. 144-155 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] L.Zhao: "Approximating the minimum k-way cut in a graph via minimum 3-way cuts"J.Combinatorial Optimization. vol.5. 397-410 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Hasunuma: "Independent spanning trees with small depths in iterated line digraphs"Discrete Applied Mathematics. vol.110. 189-212 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "Minimum cost source location problem with vertex-connectivity requirements in digraphs"Information Processing Letters. vol.80,no.6. 287-294 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "Bounds on sum number in graphs"Discrete Mathematics. vol.240,no.1-3. 175-185 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] L.Zhao: "A note on approximating the survivable network design problem in hypergraphs"Inst.Electron.Inform.Comm.Eng.Trans.Fundamentals. vol.E85-D,no.2. 322-326 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Fujito: "A 2-approximation algorithm for the minimum weight edge dominating set problem"Discrete Applied Mathematics. vol.118,no.3. 199-208 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Nagamochi: "An efficient NC algorithm for a sparse k-edge-connectivity certificate"J.Algorithms. vol.38,no.2. 354-373 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 今井桂子: "離散構造とアルゴリズムVI"近代科学社. 215 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 杉原厚吉: "アルゴリズム工学-計算困難問題への挑戦-"共立出版. 280 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "Convexity of elementary flow game"Trans. Inst. Electron. Inform. Comm. Eng. Jap.. vol.J81-D-I, no.6. 666-676 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A. Frank: "Two arc-disjoint paths in Eulerian digraphs"SIAM J. Disc. Math.. vol.11, no.4. 557-589 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Ibaraki: "A fast algorithm for finding a maximum free multiflow in an inner Eulerian network and some generalizations"Combinatorica. vol.18, no.1. 61-83 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "A note on minimizing submodular functions"Information Processing Letters. vol.67. 239-244 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Ishii: "Optimal augmentation of a biconnected graph to a k-edge-connected and triconnected graph"Proceedings 9th Annual ACM-SIAM Symposium on Discrete Algorithms. 280-289 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Hasunuma: "Independent spanning trees with small depths in iterated line digraphs"Australian Computer Science Communications. vol.20, no.3. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "Edge-splitting and edge-connectivity augmentation in planar graphs"Lecture Notes in Computer Science. 1412. 96-111 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Y. Karuno: "A 1.5-approximation for single-vehicle scheduling problem on a line with release and handling times"Japan-U.S.A. Symposium on Flexible Automation. 1363-1366 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Ishii: "k-edge and 3-vertex connectivity augmentation in an arbitrary multigraph"Lecture Notes in Computer Science. vol.1533. 159-168 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "Polyhedral structure of submodular and posi-modular systems"Lecture Notes in Computer Science. vol.1533. 169-178 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "An efficient NC algorithm for a sparse k-edge-connectivity certificate"Lecture Notes in Computer Science. vol.1533. 447-456 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "Augmenting edge-connectivity over the entire range in 0(nm) time"J. Algorithms. vol.30. 253-301 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "Augmenting a submodular and posi-modular set function by a multigraph"Proceedings of the 1st Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications. 273-279 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "A fast algorithm for computing minimum 3-way and 4-way cuts"Lecture Notes in Computer Science. vol.1610. 377-390 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Ishii: "Augmenting an (1-1)-vertex-connected multigraph to a k-edge-connected and 1-vertex-connected multigraph"Lecture Notes in Computer Science. vol.1643. 414-425 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "An approximation for finding a smallest 2-edge-connected subgraph containing a specified spanning tree"Lecture Notes in Computer Science. vol.1627. 31-40 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "A faster algorithm for computing minimum 5-way and 6-way cuts in graphs"Lecture Notes in Computer Science. vol.1627. 164-173 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "Bisecting two subsets in 3-connected graphs"Lecture Notes in Computer Science. vol.1741. 425-434 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] L. Zhao: "Approximating the minimum k-way cut in a graph via minimum 3-way cuts"Lecture Notes in Computer Science. vol.1741. 373-382 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "An approximation of the minimum vertex cover in a graph"J. of Japan Society for Industrial and Applied Mathematics. vol.16, no.3. 369-375 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] X. Deng: "Algorithmic aspects of the core of combinatorial optimization games"Math. of Operations Research. vol.24, no.3. 751-766 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "A simple proof of a minimum cut algorithm and its applications"Inst. Electron. Inform. Comm. Eng. Trans. Fundamentals. vol.E82-A, no.10. 2231-2236 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] P. Eades: "Drawing clustered graphs on an orthogonal grid"Journal of Graph Algorithms and Application. vol.3, no.4. 3-29 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "A simplified 0(nm) time edge-splitting algorithm in undirected graphs"Algorithmica. vol.26. 56-67 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "Recent development of graph connectivity augmentation algorithms"Inst. Electron. Inform. Comm. Eng. Trans. Fundamentals. vol.E83-D, no.3. 372-383 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Ishii: "Optimal augmentation of a 2-vertex-connected multigraph to a k-edge-connected and 3-vertex-connected multigraph"J. Combinatorial Optimization. vol.4. 35-78 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "A fast algorithm for cactus representations of minimum cuts"J. of Japan Society for Industrial and Applied Mathematics. vol.17. 245-264 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "A faster algorithm for computing minimum 5-way and 6-way cuts in graphs"J. Combinatorial Optimization. vol.4. 151-169 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "A 7/3-approximation for the minimum weight 3-connected spanning subgraph problem"Inst. Electron. Inform. Comm. Eng. Trans. Fundamentals. vol.E83-A, no.4. 687-691 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "A fast algorithm for computing minimum 3-way and 4-way cuts"Mathematical Programming. vol.88, no.3. 507-520 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] X. Deng: "Totally balanced oombinatorial optimization games"Mathematical Programming, Series A. vol.87. 441-452 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "Polyhedral structure of submodular and posi-modular systems"Discrete Applied Mathematics. vol.107. 165-189 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Ishii: "On the minimum augmentation of an 1-connected graph to a k-connected graph"Lecture Notes in Computer Science. vol.1851. 286-299 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Ishii: "Simultaneous augmentation of two graphs to an 1-edge-connected graph and a biconnected graph"Lecture Notes in Computer Science. vol.1969. 326-337 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] L. Zhao: "A primal-dual approximation algorithm for the survivable network design problem in hypergraphs"Lecture Notes in Computer Science. vol.2010. 478-489 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Y. Karuno: "A 2-approximation algorithm for the multi-vehicle scheduling on a path with release and handling times"Lecture Notes in Computer Science. vol.2161. 218-229 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Y. Karuno: "A polynomial time approximation scheme for the multi-vehicle scheduling on a path with release and handling times"Lecture Notes in Computer Science. vol.2223. 36-47 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "On the minimum local-vertex-connectivity augmentation in graphs"Lecture Notes in Computer Science. vol.2223. 124-135 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] L. Zhao: "A unified framework for approximating some partition problems via greedy splitting"Lecture Notes in Computer Science. vol.2223. 682-694 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "Augmenting a submodular and posi-modular set function by a multigraph"J. Combinatorial Optimization. vol.5, no.2. 175-212 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "An efficient NC algorithm for a sparse k-edge-connectivity certificate"J. Algorithms. vol.38, no.2. 354-373 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "Solving the single-vehicle scheduling problem for all home locations under depth-first routing on a tree"Inst. Electron. Inform. Comm. Eng. Trans. Fundamentals. vol.E84-A, no.5. 1135-1143 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Ishii: "Multigraph augmentation under biconnectivity and general edge-connectivity requirements"Networks. vol.37, no.3. 144-155 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] L. Zhao: "Approximating the minimum k-way cut in a graph via minimum 3-way cuts"J. Combinatorial Optimization. vol.5. 397-410 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Hasunuma: "Independent spanning trees with small depths in iterated line digraphs"Discrete Applied Mathematics. vol.110, no.2. 189-212 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "Minimum cost source location problem with vertex-connectivity requirements in digraphs"Information Processing Letters. vol.80, no.6. 287-294 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Nagamochi: "Bounds on sum number in graphs"Discrete Mathematics. vol.240, no.1-3. 175-185 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] L. Zhao: "A note on approximating the survivable network design problem in hypergraphs"Inst. Electron. Inform. Comm. Eng. Trans. Fundamentals. vol.E85-D, no.2. 322-326 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Fujito: "A 2-approximation algorithm for the minimum weight edge dominating set problem"Discrete Applied Mathematics. vol.118, no.3. 199-208 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 永持仁: "初等的フローゲームの凸小生について"電子情報通信学会論文誌. J81-D-I. 666-676 (1998)

    • Related Report
      2000 Annual Research Report
  • [Publications] A.Frank: "Two-arc-disjoint paths on Eulerian digraphs"SIAM J.Discrete mathematics. 11. 557-589 (1998)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Ibaraki: "A fast algorithm for finding a maximum free multiflow in an Eulerian network and some generalization"Combinatorica. 18. 61-83 (1998)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.nagamochi: "A note on minimizing submodular functions"Information Processing Letters. 67. 239-244 (1998)

    • Related Report
      2000 Annual Research Report
  • [Publications] H,Nagamochi: "Augmenting edge-connectivity over the range in o(nm) time"J.Algorithms. 30. 253-301 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] H,Nagamochi: "An approximation of the minimum vertex cover in a graph"J.Japan Society for Industrial and Applied Mathematics. 16. 369-375 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] H,Nagamochi: "A fast algorithm for cactus representations of minimum cuts"J.of Japan Society for Industrial and Applied Mathematics. 17. 245-264 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] H,Nagamochi: "A faster algorithm for computing minimum 5-way and 6-way cuts in graphs"J.Combinatorial Optimization. 4. 151-169 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] H,Nagamochi: "A7/3-approximation for the minimum weight 3-connected spanning subgraph problem"Inst.Electron,Inform,Comm.Eng.Trans.Fundamentals. E83-A. 687-691 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] H,Nagamochi: "A fast algorithm for computing minimum 3-way and 4-way cuts"Mathematical Programming. 88. 507-520 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] X,Deng: "Totally balanced combinatorial optimization games"Mathematical Programming,Series A. 87. 441-452 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] H,Nagamochi: "Polyhedral structure of submodular and posi-modular systems"Discrete Applied Mathematics. 107. 165-189 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] X.Deng: "Algorithmic aspects of the ure of combinatorial optimization games"Math.of Operations Research. 24. 751-766 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] H,Nagamochi: "A simple prout of aminimum cut algorithm and its applications"Inst.Electron.Inform,Comm.Eng.Trans.Fund. E82-A. 2231-2236 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] P,Eades: "Drawing clustered graphs on an orthogonal grid"J.Graph Algorithms and Application. 3. 3-29 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Nagamochi: "A simplified O(nm) time eoye-splitting algorithm in undirected graphs"Algorithmica. 26. 56-67 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] H,Nagamochi: "Recent development of graph connectivity angmentation algorithms"Inst.Electron.Inform.Comm..Eng.Trans,Fundamentals.. E83-D. 372-383 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Ishii: "Optimal angmentation of a2-rertex-connected multigraph to a k-edge-connected and 3-rertex-connected multigraph"J.Combinatorial Optimization. 4. 35-78 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Ishii: "k-edge and 3-rertex connectivity angmentation in an arbitrary multigraph."Lecture Notes in Computer Science. 1533. 159-168 (1998)

    • Related Report
      2000 Annual Research Report
  • [Publications] H,Nagamochi: "Polyhedral structure of submodular and posi-modular systems"Lecture Notes in Computer Science. 1533. 169-178 (1998)

    • Related Report
      2000 Annual Research Report
  • [Publications] H,Nagamochi: "An efficient NC algorithm for asparse k-edge-connectivity certificate"Lecture Notes in Computer Science. 1533. 447-456 (1998)

    • Related Report
      2000 Annual Research Report
  • [Publications] H,Nagamochi: "A fast algor thin that for computing minimum 3-way and 4-way cuts"Lecture Notes in Computer Science. 1610. 377-390 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Ishii: "Augmenting an (l-1)-vertex-connected multigraph to a k-edge-connected and l-vertex-connected multigraph"Lecture Notes in Computer Science. 1643. 414-425 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] H,Nagamochi: "An approximation for finding a smallest 2-edge-connected subgraph containing a specified spanning tree"Lecture Notes in Computer Science. 1627. 31-40 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] H,Nagamochi: "A faster algorithm for computing minimum 5-way and 6-way cuts in graphs"Lecture Notes in Computer Science. 1627. 164-173 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] H,Nagamochi: "Bisecting two suboets in 3-connected graphs"Lecture Notes in Computer Science. 1741. 425-434 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] L.Zhao: "Approximating the minimum k-way cut in a graph via minimum 3-way cuts"Lecture Notes in Computer Science. 1741. 373-382 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Ishii: "On the minimum angmentation of an l-connected graph to a k-connected graph"Lecture Notes in Computer Science. 1851. 286-299 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Ishii: "Simultaneous angmentation of two graphs to an l-edge-connected graph and a biconnected graph. and a biconnected graphs"Lecture Notes in Computer Science. 1969. 326-337 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] L.Zhao: "A primal-dual approximation algorithm for the survivable network design problem in hyper graphs"Lecture Notes in Computer Science. 2010. 478-489 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] H,Nagamochi: "solving the single-vehicle scheduling problem for all home locations under depth-first rouling on a tree"Inst,Electron.Inform.Comm.Eng.Trans,Fundamentals. (掲載決定).

    • Related Report
      2000 Annual Research Report
  • [Publications] T,Fujito: "A 2-approximation algorithm for the minimum weightedge dominating set problem"Discrete Applied Mathematics. (掲載決定).

    • Related Report
      2000 Annual Research Report
  • [Publications] H,Nagamochi: "Bisecting two subsets in 3-connected graphs"Combinatorica. (掲載決定).

    • Related Report
      2000 Annual Research Report
  • [Publications] H,Nagamochi: "Minimum cost source location problem with vertex-connectivity requirements in digraphs"Information Processing Letters. (掲載決定).

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Hasunama: "Independent spanning trees with small depths in terated line digraphs"Discrete Applied Mathematics. (掲載決定).

    • Related Report
      2000 Annual Research Report
  • [Publications] L,Zhao: "Approximating the minimum k-way cut in a graph via minimum 3-way cuts"J.Combinatorial Optimization. (掲載決定).

    • Related Report
      2000 Annual Research Report
  • [Publications] H,Nagamochi: "Angmenting a submodular and posi-modular set function by a multigraph"J.Combinatorial Optimization. (掲載決定).

    • Related Report
      2000 Annual Research Report
  • [Publications] H,Nagamochi: "An efficient NC algorithm for a sparse k-edge connectivity certificate"J.Algorithm. (掲載決定).

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Ishii: "Multigraph angmentation under biconnectivity and general edge-connectivity requirements"Networks. (掲載決定).

    • Related Report
      2000 Annual Research Report
  • [Publications] H,Nagamochi: "Graph connectivity and its angmentation : application of MA orderings"Discrete Applied Mathematics. (掲載決定).

    • Related Report
      2000 Annual Research Report
  • [Publications] 永持仁: "離散構造とアルゴリズムVI第3章"藤重悟編,近代科学者. 39 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] H. Nagamochi: "Augmenting edge-connectivity over the entire range in δ(nm) time"J. Algorithms. 30. 253-301 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] H. Nagamochi: "An approximation of the minimum vertex cover in a graph"J. of Japan Society for Industrial and Applied Math.. 16. 369-375 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] X. Deng: "Algorithmic aspects of the core of combinatorial optimization games"Math. of Operations Research. 24. 751-766 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] H. Nagamochi: "A Simple proof of a minimum cut algorithm and its applications"Inst. Electron. Inform, Comm, Eng. Trans, Fundamentals. E82-A. 2231-2236 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] P. Eades: "Drawing clustered graphs on an orthogonal grid"J. Graph Algorithms and Application. 3. 3-29 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] H. Nagamochi: "A simplified o(nm) time edge-splitting algorithm in undirected graphs"Algorithmica. 26. 56-67 (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] H. Nagamochi: "A fast algorithm for computing minimum 3-way and 4-way cuts"Lecture Notes in Computer Science, Springer-Verlag. 1610. 377-390 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] T. Ishii: "Augmenting an (l-1)-vertex-connected multigraph to a k-edge-connected and l-vertex-connected multigraph"Lecture Notes in Computer Science, Springer-Verlag. 1643. 414-425 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] H. Nagamochi: "An approximation for finding a smallest 2-edge-connected Subgraph containing a specified spanning tree"Lecture Notes in Computer Science, Springer-Verlag. 1627. 31-40 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] H. Nagamochi: "A faster algorithm for computing minimum 5-way and 6-way cuts in graphs"Lecture Notes in Computer Science, Springer-Verlag. 1627. 164-173 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] H. Nagamochi: "Bisecting two subsets in 3-connected graphs"Lecture Notes in Computer Science, Springer-Verlag. 1741. 425-434 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] L. Zhao: "Approximating the minimum ktway cut in a graph via minimum 3-way cuts"Lecture Notes in Computer Science, Springer-Verlag. 1741. 373-382 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] T. Ishii: "Optimal angmeutation of a 2-vertex-connected multigraphr to a K-edge- connected and 3-vertex-connected multigraph"J. Combinatorial Optimization. (発売予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] H. Nagamochi: "A fast algorithm for cactus representations of minimum cuts"J. of Japan Society for Industrial and Applied Math. (発売予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] H. Nagamochi: "A 7/3-approximation for the minimum weight 3-conhecteal Spanning subgraph problem"Inst. Electron, Inform, Comm. Eng. Trans, Fund.. (発売予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] H. Nagamocbi: "Polyhealral structure of submodular and posi-modular systems"Discrete Applied Mathematics. (発売予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] X. Deng: "Totally balanced combinatorial optimization games"Mathematical Programming. (発売予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] H. Nagamochi: "Recent deuelopment of graph connectivity augmentation algorithms"Inst. Electron. Inform, Comm. Eng. Trans. Fund.. (発売予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] 永持仁: "離散構造とアルゴリズムVI、第3章"近代科学社. 39 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 永持,牧野,曽,村田,茨木: "初等的フローゲームの凸性について" 電子情報通信学会論文誌. J81-D-I. 666-676 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] A.Frank,T.Ibaraki,H.Nagamochi: "Two Arc-Disjoint Paths in Eularian Digraphs" SIAM J.Dicrete Mathematics. 11. 557-589 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Ibaraki,A.Karzanov,H.Nagamochi: "A Fast Algorithm for Finding a Maximum Free Multiflow in an Inner Eulerian Network and Some Generalizations" Combinatorica. 18. 61-83 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Nagamochi,T.Ibaraki: "A Note on Minimizing Submodular Functions" Information Processing Letters. 67. 239-244 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Ishii,H.Nagamochi,T.Ibaraki: "Optimal Augmentation of a Biconnected Graph to nk-Edge-Connected an Tri-Conne grup〓" Proc.9th ACM-SIAM Symp.on Discrete Algorithms. 280-289 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Hasunuma,H.Nagamochi: "Independent Spanning Trees with Small Depths in Iterated Line Digraphs" Australian Computer Science Communications,Computing Theory. 20. 21-35 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Nagamochi,P.Eades: "Edge-Splitting and Edge-Connectivity Augmentation in Planar Graphs" Lecture Notes in Computer Science. 1412. 96-111 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Y.Karuno,H.Nagamochi,T.Ibaraki: "A 1.5-Approxination for Single-Vehicle Scheduling Problem on a Line with Release and Handling Times" Proc.Japan-U.S.A.Symp.on Flexible Automation. 1363-1366 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Ishii,H.Nagamochi,T.Ibaraki: "k-Edge and 3-Vertex Connectivity Augmentation in an Arbitrary Multigraph" Lecture Notes in Computer Science. 1533. 159-168 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Nagamochi,T.Ibaraki: "Polyhedral Structure of Submodular and Posi-modular Systems" Lecture Notes in Computer Science. 1533. 169-178 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Nagamochi,T.Hasunuma: "An Efficient NC Algorithm for a Sparse k-Edge-Connectivity Certificate" Lecture Notes in Computer Science. 1533. 447-456 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Nagamochi,T.Ibaraki: "A Fast Algorithm for Computing Minimum 3-Way and 4-Way Cuts" Lecture Note in Computer Science,IPC099. (発表予定). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Nagamochi,T.Ibaraki: "Augmenting Edge-Connectivity over the Entite Range in O(nm) Time" J.Algorithms. 30. 253-301 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Nagamochi,T.Ibaraki: "An Approximation of the Minimum Vertex Cover in a Graph" J.Japan Society for Industrial and Applied Math.(掲載予定). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 岩野和生,加藤直樹,永持 仁: "アルゴリズム入門-設計と解析-(Computer Algorithms,sara Baaseの訳書)" アジソン・ウエスレイ社, 439 (1998)

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Published: 1998-04-01   Modified: 2016-04-21  

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