Edge-Connectivity Augmentation Preserving Simplicity
نویسندگان
چکیده
Given a simple graph G = (V,E), our goal is to find a smallest set F of new edges such that G = (V,E ∪ F ) is k-edge-connected and simple. Recently this problem was shown to be NP-complete. In this paper we prove that if OPT P is high enough—depending on k only—then OPT S = OPT P holds, where OPT S (OPT P ) is the size of an optimal solution of the augmentation problem with (without) the simplicity-preserving requirement, respectively. Furthermore, OPT S − OPT P ≤ g(k) holds for a certain (quadratic) function of k. Based on these facts an algorithm is given which computes an optimal solution in time O(n) for any fixed k. Some of these results are extended to the case of nonuniform demands as well.
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