Design of Dynamic Algorithms via Primal-Dual Method

Abstract : We develop a dynamic version of the primal-dual method for optimization problems, and apply it to obtain the following results. (1) For the dynamic set-cover problem, we maintain an O(f 2)-approximately optimal solution in O(f · log(m + n)) amortized update time, where f is the maximum "frequency" of an element, n is the number of sets, and m is the maximum number of elements in the universe at any point in time. (2) For the dynamic b-matching problem, we maintain an O(1)-approximately optimal solution in O(log 3 n) amortized update time, where n is the number of nodes in the graph.
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https://hal.inria.fr/hal-01964700
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Sayan Bhattacharya, Monika Henzinger, Giuseppe Italiano. Design of Dynamic Algorithms via Primal-Dual Method. ICALP 2018 - International Colloquium on Automata, Languages, and Programming, Jul 2015, Kyoto, Japan. pp.206-218, ⟨10.1007/978-3-662-47672-7_17⟩. ⟨hal-01964700⟩

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