Computing the map of geometric minimal cuts

Abstract

In this paper we consider the problem of computing a map of geometric minimal cuts (called MGMC problem) induced by a planar rectilinear embedding of a subgraph H=(V H , E H ) of an input graph G. We first show that unlike the classic min-cut problem on graphs, the number of all rectilinear geometric minimal cuts is bounded by a low polynomial, O(n 3). Our algorithm for identifying geometric minimum cuts runs in O(n 3 logn (loglogn)3) time in the worst case which can be reduced to O(n logn (loglogn)3) when the maximum size of the cut is bounded by a constant, where n=|V H |. Once geometric minimal cuts are identified we show that the problem can be reduced to computing the L ∞ Hausdorff Voronoi diagram of axis aligned rectangles. We present the first output-sensitive algorithm to compute this diagram which runs in O((N+K)log2 N loglogN) time and O(Nlog2 N) space, where N is the number of rectangles and K is the complexity of the diagram. © 2009 Springer-Verlag Berlin Heidelberg.