Abstract
Max-flow in planar graphs has always been studied with the assumption that there are capacities only on the edges. Here we consider a more general version of the problem when the vertices as well as edges have capacity constraints. In the context of general graphs considering only edge capacities is not restrictive, since the vertex-capacity problem can be reduced to the edge-capacity problem. However, in the case of planar graphs this reduction does not maintainplanarity and cannot be used. We study different versions of the planar flow problem (all of which have been extensively investigated in the context of edge capacities).
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Communicated by Harold N. Gabow.
A preliminary version of this paper appeared in theProceedings of the First Integer Programming and Combinatorial Optimization Conference, Waterloo, Canada, May 1990, pp. 367–383. Samir Khuller is currently supported by NSF Grant CCR-8906949. Part of this research was done while he was visiting the IBM Thomas J. Watson Research Center and was supported by an IBM Graduate Fellowship at Cornell University. Joseph Naor's work was supported by Contract ONR N00014-88-K-0166 while he was a post-doctoral fellow in the Department of Computer Science at Stanford University.
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Khuller, S., Naor, J.(. Flow in planar graphs with vertex capacities. Algorithmica 11, 200–225 (1994). https://doi.org/10.1007/BF01240733
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DOI: https://doi.org/10.1007/BF01240733