An exact algorithm for MAX-CUT in sparse graphs

Federico Della Croce (1) , Marcin J. Kaminski (2) , Vangelis Th. Paschos (3)

1 DAI
2 RUTCOR - Rutgers Center for Operations Research
3 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

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.

Domaines: Complexité [cs.CC]; Recherche d'information [cs.IR]

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