The max-flow problem in planar networks with only edge capacities has been proved to be in NC (Nickle's Class). This paper considers a more general version of the problem when the nodes as well as the edges have c...The max-flow problem in planar networks with only edge capacities has been proved to be in NC (Nickle's Class). This paper considers a more general version of the problem when the nodes as well as the edges have capacities. In a general network, the node-edge-capacity problem can be easily reduced to the edge-capacity problem. But in the case of planar network this reduction may destroy the planarity, and reduces the problem to the edge-capacity problem in a general network, which is P-complete. A recent contribution presents a new reduction for planar networks, that maintains the planarity. In this paper, it is proved that this reduction is in NC and thus the node-edge-capacity problem in undirected planar networks is in NC. Keywords parallel algorithm - NC (Nickle's Class) algorithm, max-flow Supported by the National Basic Research 973 Program of China under Grant No.G1999032700.展开更多
文摘The max-flow problem in planar networks with only edge capacities has been proved to be in NC (Nickle's Class). This paper considers a more general version of the problem when the nodes as well as the edges have capacities. In a general network, the node-edge-capacity problem can be easily reduced to the edge-capacity problem. But in the case of planar network this reduction may destroy the planarity, and reduces the problem to the edge-capacity problem in a general network, which is P-complete. A recent contribution presents a new reduction for planar networks, that maintains the planarity. In this paper, it is proved that this reduction is in NC and thus the node-edge-capacity problem in undirected planar networks is in NC. Keywords parallel algorithm - NC (Nickle's Class) algorithm, max-flow Supported by the National Basic Research 973 Program of China under Grant No.G1999032700.
