2004 Fiscal Year Final Research Report Summary
Construction of Approximation Algorithms Based on Graph Theory and Its Application to Network Problems
| Project/Area Number |
14580372
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
計算機科学
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| Research Institution | Kyoto University (2004)
Toyohashi University of Technology (2002-2003) |
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Principal Investigator |
NAGAMOCHI Hiroshi Kyoto University, Department of Applied Mathematics and Physics, Professor, 情報学研究科, 教授 (70202231)
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| Co-Investigator(Kenkyū-buntansha) |
ISHII Toshimasa Toyohashi University of Technology, Department of Information and Computer Science, Assistant Professor, 工学部, 助手 (30324487)
KARUNO Yoshiyuki Kyoto Institute of Technology, Department of Mechanical and System Engineering, Associate Professor, 工芸学部, 助教授 (80252542)
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| Project Period (FY) |
2002 – 2004
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| Keywords | graph connectivity / polynomial algorithm / approximation algorithm / network problem / maximum flow problem / vertex connectivity / edge connectivity / maximum adjacency order |
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| Research Abstract |
By using sparsification technique by maximum adjacency order, we obtained an O(n^2(1+min{κ^2, κ√<n>}/δ)) time and O(-n+m) space algorithm that computes a 2-approximation solution for the problem of finding a minimum vertex cut in a graph G, where n,m,κ and δ denote the number of vertices, the number of edges, the vertex-connectivity and the minimum degree in G, respectively.
For the problem of finding a minimum (s,t)-cut in a digraph with a source s and a sink t, we introduced a new parameter μ that measures undirectedness of a given digraph, and gave an O(min{m+ν(ν+μ)^<1/2>n,(ν+μ)^<1/6>nm^<2/3>}}) time algorithm, where ν denotes the size of a minimum (s,t)-cut.
For the problem of augmenting a given connected graph to meet biconnectivity between a prescribed pair, we designed a linear time 4/3-approximation algorithm.
We also surveyed a recent progress on graph algorithms for network connectivity problems. We showed that the extreme set problem, the cactus representation problem, the edge-connectivity augmentation problem and the source location problem can be solved in O(mn+n^2log n) time by using maximum adjacency order.
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Research Products
(32 results)
