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Algorithms - ESA 2003: 11th Annual European Symposium, by Bernard Chazelle (auth.), Giuseppe Di Battista, Uri Zwick

By Bernard Chazelle (auth.), Giuseppe Di Battista, Uri Zwick (eds.)

This publication constitutes the refereed court cases of the eleventh Annual eu Symposium on Algorithms, ESA 2003, held in Budapest, Hungary, in September 2003.

The sixty six revised complete papers provided have been rigorously reviewed and chosen from one hundred sixty five submissions. The scope of the papers spans the whole variety of algorithmics from layout and mathematical research concerns to real-world functions, engineering, and experimental research of algorithms.

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Extra resources for Algorithms - ESA 2003: 11th Annual European Symposium, Budapest, Hungary, September 16-19, 2003. Proceedings

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An α-approximation algorithm is one that runs in polynomial time and always returns an α-approximate solution. One primary theme of this line of research is to exploit a classical linear programming (LP) relaxation of the problem, initially proposed by Balinski [4]. We contribute to this vein by shedding new light on two existing UFL algorithms, the primal-dual algorithm of Jain & Vazirani (JV) [15], and the algorithm of Mettu & Plaxton (MP) [21]. Supported by the Fannie and John Hertz Foundation and by NSF grant CCR-0113371.

G. Kroon, A. Sen, H. Deng and A. Roy The optimal cost chromatic partition problem for trees and interval graphs. Graph Theoretical Concepts in Computer Science WG 96, Como, LNCS, 1996. 10. E. Kubicka The chromatic sum of a graph. D. thesis, Western Michigan University, 1989. 11. E. Kubicka, G. Kubicki, and D. Kountanis. Approximation Algorithms for the Chromatic Sum. Proc. , Springer LNCS 507, 15–21, 1989. 12. E. Kubicka and A. J. Schwenk An introduction to chromatic sums. Proceedings of the seventeenth Annual ACM Comp.

Thus, every feasible solution for the original k-median LP is also feasible for its Lagrangian relaxation, and the objective function value in the relaxation is no greater than in the original LP. Therefore, every dual feasible solution for the Lagrangian relaxation provides a lower bound on the optimal k-median solution. These observations lead to the following result in [15]. Theorem 2 Suppose that we set all facility costs to z > 0, so that the JV algorithm opens exactly k facilities. Then this is a 3-approximate k-median solution.

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