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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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2005: ¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 2004: ¥1,700,000 (Direct Cost: ¥1,700,000)
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| Keywords | graphs / networks / connectivity / enumeration / cliques / the Internet / location problems / communities / 多項式時間アルゴリズム / 孤立 / 連結度増大問題 / 領域グラフ / 枝連結度 / 多項式時問アルゴリズム / H-彩色問題 / 階層構造 / NP完全 / ルーチング |
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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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Report
(3 results)
Research Products
(28 results)
