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

• Published in: Journal of computer science and technology Vol. 19; no. 6; pp. 787 - 790
• Main Authors: Zhang, Xian-Chao, Wan, Ying-Yu, Chen, Guo-Liang
• Format: Journal Article
• Language: English
• Published: Beijing Springer Nature B.V 01.12.2004; National High Performance Computing Center at He fei, Department of Computer Science and Technology University of Science and Technology of China, Hefei 230027, P.R. China
• Subjects: Networks; Nodes; Numerical control; Reduction; parallel algorithm; NC (Nickle's Class) algorithm; max-flow
• ISSN: 1000-9000; 1860-4749
• DOI: 10.1007/BF02973440

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.