2002 Fiscal Year Final Research Report Summary
A Study on Approximation Algorithm Design Based on Linear Program
| Project/Area Number |
13680409
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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 | NAGOYA UNIVERSITY |
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Principal Investigator |
FUJITO Toshihiro NAGOYA UNIV., ASSCE. Prot. Graduate School of Engineering, 工学系研究科, 助教授 (00271073)
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| Project Period (FY) |
2001 – 2002
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| Keywords | NP-hard problem / Approximation Algorithm / Packing Problem / Covering problem / Greedy heuristic / Edge Dominating Set problem / Set Cover problem / Linear program relaxation |
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| Research Abstract |
The main purpose of the current research is to develop approximation algorithms of high quality, based on linear program relaxation, for computationally hard combinatorial optimization problems. The summary of major outcomes Is as follows : 1. Polymatroid packing and covering were shown to be approximable, by modified greedy heuristics, within factors of 2/ (κ+1) and H (κ) - 1/6, respectively. 2. The minimum cost edge dominating set problem was shown to be approximable within 21/(10) by reduction to edge cover, and within 2 by a larger scale linear relaxation. 3. It was shown that (1) minimum cost maximal matching cannot be approximated within any polynomially computable factor (assuming P ≠ NP), (2) minimum cost connected edge dominating set is approximable within 3+ε, (3) minimum cost connected vertex cover can be approximated witliin In n+3, but cannot be within (l-ε) In n (assuming NP 〓 DTIME (n^<O(log log n)>)). 4. A 2-approximation NC (and RNC) algorithm was developed for connected vertox cover and counected edge dominating etset. 5. The capacitated partial vertex cover problem with demands was shown to be approximable within a factor of 2. 6. The binary weighted κ-set cover problem was considered. For costs 1 and ω with ω 【greater than or equal】 1.5, 3-set cover was shown approximable within H (3) - 1/6, and for costs 1 and 2, κ-set cover within H (κ) -1/12, where H (κ) denotes Σ^κ_<i=I> 1/i.
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Research Products
(14 results)
