|Budget Amount *help
¥1,200,000 (Direct Cost : ¥1,200,000)
Fiscal Year 2002 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 2001 : ¥700,000 (Direct Cost : ¥700,000)
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.