Abstract
Given an instance of an optimization problem and a good solution of that instance, the reoptimization is a concept of analyzing how does the solution change when the instance is locally modified. We investigate reoptimization of the following problems: Maximum Weighted Independent Set, Maximum Weighted Clique, Minimum Weighted Dominating Set, Minimum Weighted Set Cover and Minimum Weighted Vertex Cover. The local modifications we consider are addition or removal of a constant number of edges to the graph, or elements to the covering sets in case of Set Cover problem. We present the following results:
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We provide a PTAS for reoptimization of the unweighted versions of the aforementioned problems when the input solution is optimal.
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We provide two general techniques for analyzing approximation ratio of the weighted reoptimization problems.
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We apply our techniques to reoptimization of the considered optimization problems and obtain tight approximation ratios in all the cases.
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Bilò, D., Widmayer, P., Zych, A. (2009). Reoptimization of Weighted Graph and Covering Problems. In: Bampis, E., Skutella, M. (eds) Approximation and Online Algorithms. WAOA 2008. Lecture Notes in Computer Science, vol 5426. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-93980-1_16
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DOI: https://doi.org/10.1007/978-3-540-93980-1_16
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