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An exact algorithm for MAX-CUT in sparse graphs

Abstract : The MAX-CUT problem consists in partitioning the vertex set of a weighted graph into two subsets. The objective is to maximize the sum of weights of those edges that have their endpoints in two different parts of the partition. MAX-CUT is a well known NP-hard problem and it remains NP-hard even if restricted to the class of graphs with bounded maximum degree ∆ (for ∆ ≥ 3). In this paper we study exact algorithms for the MAX-CUT problem. Introducing a new technique, we present an algorithmic scheme that computes maximum cut in weighted graphs with bounded maximum degree. Our algorithm runs in time O∗(2(1−(2/∆))n). We also describe a MAX-CUT algorithm for general weighted graphs. Its time complexity is O∗(2mn/(m+n)). Both algorithms use polynomial space.
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Contributor : Marie-Hélène Hugonnard-Roche <>
Submitted on : Monday, November 27, 2006 - 11:14:11 AM
Last modification on : Wednesday, September 23, 2020 - 4:29:42 AM
Long-term archiving on: : Tuesday, April 6, 2010 - 11:26:20 PM


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  • HAL Id : hal-00116633, version 1


Federico Della Croce, Marcin Kaminski, Vangelis Paschos. An exact algorithm for MAX-CUT in sparse graphs. 2006. ⟨hal-00116633⟩



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