Titlebook: Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques; 4th International Wo Michel Goemans,Klaus Jansen,Lu

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On the Equivalence between the Primal-Dual Schema and the Local-Ratio Techniquech approach, which extend known frameworks for covering problems. We show that the two are equivalent, and conclude that the integrality gap of an integer program serves as a bound to the approximation ratio when working with the local-ratio technique.

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Assignment

A Simple Dual Ascent Algorithm for the Multilevel Facility Location ProblemWe present a simple dual ascent method for the multilevel facility location problem which finds a solution within 6 times the optimum for the uncapacitated case and within 12 times the optimum for the capacitated one. The algorithm is deterministic and based on the primal-dual technique.

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Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques978-3-540-44666-8Series ISSN 0302-9743 Series E-ISSN 1611-3349

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Anirban Chowdhury,Chaitanya Kachareistributions of instances really are, whether these distributions are mathematically defined or come from real-world applications. Frequently, NP-complete problems have been successfully attacked on “typical” instances using heuristic methods. Little is known about when or why some of these heuristics succeed.

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