Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Approximation algorithms for combinatorial problems
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Clique is hard to approximate within n1-
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Linear degree extractors and the inapproximability of max clique and chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Reoptimization of Steiner Trees
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
On the hardness of reoptimization
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Reoptimization of minimum and maximum traveling salesman's tours
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
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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: 1 We provide a PTAS for reoptimization of the unweighted versions of the aforementioned problems when the input solution is optimal. 1 We provide two general techniques for analyzing approximation ratio of the weighted reoptimization problems. 1 We apply our techniques to reoptimization of the considered optimization problems and obtain tight approximation ratios in all the cases.