Maximum Cut Problem, MAX-CUT
نویسنده
چکیده
The MAXIMUM CUT problem (MAX-CUT) is one of the simplest graph partitioning problems to conceptualize, and yet it is one of the most difficult combinatorial optimization problems to solve. The objective of MAX-CUT is to partition the set of vertices of a graph into two subsets, such that the sum of the weights of the edges having one endpoint in each of the subsets is maximum. This problem is known to be NP-complete [18, 27]; however, it is interesting to note that the inverse problem, i.e., that of looking for the minimum cut in a graph is solvable in polynomial time using network flow techniques [1]. MAX-CUT is an important combinatorial problem and has applications in many fields including VLSI circuit design [9, 32] and statistical physics [5]. For other applications, see [16, 21]. For a detailed survey of MAX-CUT, the reader can refer to [33].
منابع مشابه
An exact algorithm for MAX-CUT in sparse graphs (Preliminary version)1
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 stud...
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