# Encyclopedia of Algorithms

Living Edition
| Editors: Ming-Yang Kao

# Max Cut

• Alantha Newman
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27848-8_219-2

## Year and Authors of Summarized Original Work

• 1994; 1995; Goemans, Williamson

## 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 [20]. In fact, it is NP-hard to approximate to within a factor better than $$\frac{16} {17}$$

## Keywords

Graph partitioning Approximation algorithms
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