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Encyclopedia of Algorithms pp 489–492Cite as

Max Cut

1994; Goemans, Williamson 1995; Goemans, Williamson

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Keywords and Synonyms

Maximum bipartite subgraph    

Problem Definition

Given an undirected edge-weighted graph, \( { G=(V,E) } \), the maximum cut problem (Max-Cut) is to find a bipartition of the vertices that maximizes the weight of the edges crossing the partition. If the edge weights are non-negative, then this problem is equivalent to finding a maximum weight subset of the edges that forms a bipartite subgraph, i. e. the maximum bipartite subgraph problem. All results discussed in this article assume non-negative edge weights. Max-Cut is one of Karp's original NP-complete problems [19]. In fact, it is NP-hard to approximate to within a factor better than 16/17[16,33].

For nearly twenty years, the best-known approximation factor for Max-Cut was half, which can be achieved by a very simple algorithm: Form a set S by placing each vertex in S with probability half. Since each edge crosses the cut \( { (S, V \setminus{S}) } \)with probability half, the expected value of this cut is half...

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Authors and Affiliations

  1. Department of Algorithms and Complexity, Max-Planck Institute for Computer Science, Saarbrücken, Germany

    Alantha Newman

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  1. Alantha Newman
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL, 60208, USA

    Ming-Yang Kao Professor of Computer Science

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© 2008 Springer-Verlag

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Newman, A. (2008). Max Cut. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_219

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