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By Erik D. Demaine, Nicole Immorlica (auth.), Sanjeev Arora, Klaus Jansen, José D. P. Rolim, Amit Sahai (eds.)

This publication constitutes the joint refereed complaints of the sixth overseas Workshop on Approximation Algorithms for Optimization difficulties, APPROX 2003 and of the seventh foreign Workshop on Randomization and Approximation concepts in desktop technology, RANDOM 2003, held in Princeton, manhattan, united states in August 2003.

The 33 revised complete papers provided have been rigorously reviewed and chosen from seventy four submissions. one of the matters addressed are layout and research of randomized and approximation algorithms, on-line algorithms, complexity concept, combinatorial buildings, error-correcting codes, pseudorandomness, derandomization, community algorithms, random walks, Markov chains, probabilistic evidence structures, computational studying, randomness in cryptography, and numerous applications.

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Extra info for Approximation, Randomization, and Combinatorial Optimization.. Algorithms and Techniques: 6th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2003 and 7th International Workshop on Randomization and Appro

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If the maximum matching matches all the sub-trees, then the algorithm returns the set of trees where each tree consists of a subtree Sji , the root r matched to the subtree Sji , a shortest path from the root r to Sji , and the leftover tree L (if any) that contains the root r. We now elaborate on how the edge set of every tree is decomposed in Line 4. Consider a tree Ti rooted at r. For a node v let Tv denote the rooted subtree hanging from v. Consider an edge e = (u, v) where u is the parent of v.

Haimovich, A. Rinnooy Kan and L. Stougie. Vehicle Routing: Methods and Studies, Elsevier, 1988. 12. D. Hochbaum and D. Shmoys. A best possible approximation algorithm for the k-center problem. Mathematics of Operations Research, 10(2):180-184, 1985. 13. A. Levin, private communication, May 2003. 14. D. Shmoys, E. Tardos and K. Aardal. Approximation algorithms for facility location problems. In Proceedings of the 29th Annual ACM Symposium on Theory of Computing, 265-274, 1997. 15. D. Shmoys and E.

For every ε, there is a (4 + ε)-approximation algorithm for minmax tree cover that runs in time polynomial in the size of the graph and in log( 1ε ). Proof. When B ≥ B ∗ , Lemma 4 implies that Algorithm 2 is successful and a ktree cover of cost at most 4B is computed. 1 completes the proof. 32 5 Guy Even et al. Clustering into Stars In this section we discuss the un-rooted and rooted k-star cover problem. Here, we are given an undirected complete graph G = (V, E), a metric c on the edges of E and a parameter k > 0.

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