| Project/Area Number |
10205213
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| Research Category |
Grant-in-Aid for Scientific Research on Priority Areas (B)
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| Allocation Type | Single-year Grants |
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| Research Institution | Toyohashi University of Technology (TUT) (2000-2001)
Kyoto University (1998-1999) |
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Principal Investigator |
NAGAMOCHI Hiroshi Toyohashi University of Technology, Dept. Information and Computer Sciences, Professor, 工学部, 教授 (70202231)
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| Co-Investigator(Kenkyū-buntansha) |
ISHII Toshimasa Toyohashi University of Technology, Dept. Information and Computer Sciences, Assistant Professor, 工学部, 助手 (30324487)
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| Project Period (FY) |
1998 – 2000
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| Project Status |
Completed (Fiscal Year 2001)
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| 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)
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| Keywords | graph 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 |
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| 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.
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