Computing the Map of Geometric Minimal Cuts

Authors:
Jinhui Xu;Lei Xu;Evanthia Papadopoulou
Affiliations:
Department of Computer Science and Engineering, State University of New York at Buffalo, Buffalo, USA NY 14260;Department of Computer Science and Engineering, State University of New York at Buffalo, Buffalo, USA NY 14260;Faculty of Informatics, Università della Svizzera italiana, Lugano, Switzerland CH 6904
Venue:
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Year:
2009

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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 驴 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.