2005 Fiscal Year Final Research Report Summary
Research on Modeling of the Internet Problems and Efficient Algorithms
| Project/Area Number |
16500010
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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 |
Fundamental theory of informatics
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| Research Institution | Kyoto University |
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Principal Investigator |
ITO Hiro Kyoto University, Graduate School of Informatics, Associate Professor, 情報学研究科, 助教授 (50283487)
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| Co-Investigator(Kenkyū-buntansha) |
IWAMA Kazuo Kyoto University, Graduate School of Informatics, Professor, 情報学研究科, 教授 (50131272)
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| Project Period (FY) |
2004 – 2005
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| Keywords | graphs / networks / connectivity / enumeration / cliques / the Internet / location problems / communities |
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| Research Abstract |
1. Maximum-Cover Source Location Problems
For a given graph G=(V,E) with n vertices and m edges and positive integers k and p, the maximum-cover source location problem is a problem of finding a vertex subsets (sources) S consisting of at most p vertices maximizing the number of covered vertices by S, where a vertex v is called "covered by S" if the edge-connectivity between S and v is at least k. This problem has applications of locating mirror servers on the Internet. For this problem we obtain the following results : (1) an O(np+m+nlogn) time algorithm for k at most 2, (2) an O(nm+n^2 logn) time algorithm for G of k-1 edge connected, (3) an O(knp^2) time algorithm for G of trees.
2. Enumerating Isolated Cliques
Problem of finding dense subgraphs from a graph has a close relation to the Internet search problems and recently attracts considerable attention. However, almost such problems are hard, e.g., NP-hard even for approximation. We pay attention to that for such applications we should find subgraphs not only dense inside but also sparse between outside, and we introduce an idea of "isolation," i.e., a subgraph S with k vertices is c-isolated if there exists less than ck edges S and the outside of S, where c is called an "isolation factor." We presented an O(c^5 2^{2c}m) time algorithm for enumerating all c-isolated subgraphs from a given graph with n vertices and m edges. From this, we directly obtain that we can enumerate all c-isolated graphs in lenear time if c is a constant, and polynomial time if c=O(logn). We also show that these bounds are tight.
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