Network flow and 2-satisfiability Article Received: 20 August 1991 Revised: 03 January 1992 DOI :
10.1007/BF01240738

Cite this article as: Feder, T. Algorithmica (1994) 11: 291. doi:10.1007/BF01240738
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Abstract We present two algorithms for network flow on networks with infinite capacities and finite integer supplies and demands. The first algorithm runs inO(m√K) time on networks withm edges, whereK =O(m^{2} /log^{4} m ) is the value of the optimal flow, and can also be applied to the capacitated case by lettingK be the sum of thefinite capacities alone. The second algorithm runs inO(wm logK ) time for arbitraryK , where w is a new parameter, thewidth of the network. These algorithms as well as other uses of the notion of width lead to results for several questions on the 2-satisfiability problem: minimizing the weight of a solution, finding the transitive closure, recognizing partial solutions, enumerating all solutions. The results have applications to stable matching, wherew corresponds to the number of people andm to the instance size (usuallym ≈ w^{2} ).

Key words Network flow 2-Satisfiability Communicated by Harold N. Gabow.

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Authors and Affiliations 1. Bell Communications Research Morristown USA