TY - GEN
T1 - Computing the map of geometric minimal cuts
AU - Xu, Jinhui
AU - Xu, Lei
AU - Papadopoulou, Evanthia
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/75649140586
U2 - 10.1007/978-3-642-10631-6_26
DO - 10.1007/978-3-642-10631-6_26
M3 - Conference contribution
AN - SCOPUS:75649140586
SN - 3642106307
SN - 9783642106309
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 244
EP - 254
BT - Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings
T2 - 20th International Symposium on Algorithms and Computation, ISAAC 2009
Y2 - 16 December 2009 through 18 December 2009
ER -