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- W2360752711 abstract "The minimum cut problem and maximum flow problem with both node and edge capacities in general networks can be easily reduced to the problem with only edge capacities.But the traditional reduction destroys planarity of planar networks,so in planar networks,the problems with both node and edge capacities are harder than problems with only edge capacities.The algorithms using the traditional reduction run in time O(n~(2)log()n)(where n is the number of nodes in the network).The authors have proposed a maintain-planarity reduction for the minimum cut in undirected planar networks.This paper further investigates the problems in directed planar by proposing a new maintain-planarity reduction.The new reduction leads to(O(n()log()n)-time) algorithms.In term of parallel computational complexity,the traditional reduction leads to P-completed problems,while the new reduction produces NC algorithms.It is proved that the minimum cut and maximum flow problems in directed planar networks with both node and edge capacities are both in NC." @default.
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- W2360752711 date "2006-01-01" @default.
- W2360752711 modified "2023-09-23" @default.
- W2360752711 title "Minimum Cuts and Maximum Flows in Directed Planar Networks with Both Node and Edge Capacities" @default.
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