Max-flow problem in undirected planar networks with node capacities being in NC

  • Authors:

  • Xian-Chao Zhang;Ying-Yu Wan;Guo-Liang Chen

  • Affiliations:

  • National High Performance Computing Center at Hefei, Department of Computer Science and Technology, University of Science and Technology of China, Hefei 230027, P.R. China;National High Performance Computing Center at Hefei, Department of Computer Science and Technology, University of Science and Technology of China, Hefei 230027, P.R. China;National High Performance Computing Center at Hefei, Department of Computer Science and Technology, University of Science and Technology of China, Hefei 230027, P.R. China

  • Venue:
  • Journal of Computer Science and Technology
  • Year:
  • 2004

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Abstract

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.