Abstract
In this paper, 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 \(O(f \cdot \log (m+n))\) 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.
Monika Henzinger—Supported by the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement no. 340506.
Giuseppe F. Italiano—Partially supported by MIUR under Project AMANDA.
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Bhattacharya, S., Henzinger, M., Italiano, G.F. (2015). Design of Dynamic Algorithms via Primal-Dual Method. In: Halldórsson, M., Iwama, K., Kobayashi, N., Speckmann, B. (eds) Automata, Languages, and Programming. ICALP 2015. Lecture Notes in Computer Science(), vol 9134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47672-7_17
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DOI: https://doi.org/10.1007/978-3-662-47672-7_17
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