Algorithmica

, Volume 11, Issue 3, pp 291–319

Network flow and 2-satisfiability

  • Tomás Feder
Article

DOI: 10.1007/BF01240738

Cite this article as:
Feder, T. Algorithmica (1994) 11: 291. doi:10.1007/BF01240738

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(m2/log4m) 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 ≈ w2).

Key words

Network flow2-Satisfiability

Copyright information

© Springer-Verlag New York Inc. 1994

Authors and Affiliations

  • Tomás Feder
    • 1
  1. 1.Bell Communications ResearchMorristownUSA