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Titlebook: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques; 6th International Wo Sanjeev Arora,Klaus Jansen,Am

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Wei-Ying Chou,Bi-Hui Chen,Wen-Ko ChiouThis improves the previous factor of . by Trevisan [Tre01]. For low . values we prove NP-hardness factors of . and . for 4-DM, 5-DM and 6-DM respectively. These results extend to the problem of .-Set-Packing and the problem of Maximum Independent-Set in (.+1)-claw-free graphs.
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Covering Graphs Using Trees and Starshas no more than . trees. Star covers are defined analogously. Additionally, we may also be provided with a set of . vertices which are to serve as roots of the trees or stars. In this paper, we provide constant factor approximation algorithms for finding tree and star covers of graphs, in the rooted and un-rooted versions.
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Approximating Market Equilibriaprice vector. The main tool in our algorithm is the polynomial-time algorithm of Devanur et al. [6] for a variant of the problem in which there is a clear demarcation between buyers and sellers. Their algorithm is used as a subroutine in our algorithm.
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