5 research outputs found
All-Pairs Min-Cut in Sparse Networks
Algorithms are presented for the all-pairs min-cut problem in bounded treewidth, planar, and sparse networks. The approach used is to preprocess the input n-vertex network so that afterward, the value of a min-cut between any two vertices can be efficiently computed. A tradeoff is shown between the preprocessing time and the time taken to compute min-cuts subsequently. In particular, after an Onlog Ž n. preprocessing of a bounded tree-width network, it is possible to find the value of a min-cut between any two vertices in constant time. This implies that for Ž 2 such networks the all-pairs min-cut problem can be solved in time On.. This algorithm is used in conjunction with a graph decomposition technique of Frederickson to obtain algorithms for sparse and planar networks. The running times depend upon a topological property, �, of the input network. The parameter � varies between 1 and �Ž. n; the algorithms perform well when � � on. Ž. The value Ž 2 of a min-cut can be found in time On� � log �. and all-pairs min-cut can be Ž 2 4 solved in time On � � log �. for sparse networks. The corresponding runnin
All-pairs min-cut in sparse networks
Algorithms are presented for the all-pairs min-cut problem in bounded tree-width, planar and sparse networks. The approach used is to preprocess the input -vertex network so that, afterwards, the value of a min-cut between any two vertices can be efficiently computed. A tradeoff is shown between the preprocessing time and the time taken to compute min-cuts subsequently. In particular, after an preprocessing of a bounded tree-width network, it is possible to find the value of a min-cut between any two vertices in constant time. This implies that for such networks the all-pairs min-cut problem can be solved in time . This algorithm is used in conjunction with a graph decomposition technique of Frederickson to obtain algorithms for sparse and planar networks. The running times depend upon a topological property, , of the input network. The parameter varies between 1 and ; the algorithms perform well when . The value of a min-cut can be found in time and all-pairs min-cut can be solved in time for sparse networks. The corresponding running times4 for planar networks are and , respectively. The latter bounds depend on a result of independent interest: outerplanar networks have small ``mimicking'' networks which are also outerplanar