Algorithms for the minimum partitioning problems in graphs

In this paper, the author explains the recent evolution of algorithms for minimum partitioning problems in graphs. When the set of vertices of a graph having non-negative weights for edges is divided into k subsets, the set of edges for which both endpoints are contained in different subsets is called a k-way cut or k-cut. The problem of obtaining the k-way cut that minimizes the sum of the weights is an important research topic that appears in many practical applications such as VLSI design. In this paper, the author introduces recent results including cases in which sets of terminals or sets of terminal pairs that are to be separated are further specified in this problem and cases in which the objects to be partitioned are extended from graphs to hypergraphs or submodular set functions. © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 90(10): 63– 78, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20341