2013 IEEE 54th Annual Symposium on Foundations of Computer Science (1988)

White Plains, NY, USA

Oct. 24, 1988 to Oct. 26, 1988

ISBN: 0-8186-0877-3

pp: 432-443

A.V. Goldberg , Dept. of Comput. Sci., Stanford Univ., CA, USA

ABSTRACT

A generalization of the maximum-flow problem is considered in which the amounts of flow entering and leaving an arc are linearly related. More precisely, if x(e) units of flow enter an arc e, x(e) lambda (e) units arrive at the other end. For instance, nodes of the graph can correspond to different currencies, with the multipliers being the exchange rates. Conservation of flow is required at every node except a given source node. The goal is to maximize the amount of flow excess at the source. This problem is a special case of linear programming, and therefore can be solved in polynomial time. The authors present polynomial-time combinatorial algorithms for this problem. The algorithms are simple and intuitive.

INDEX TERMS

combinatorial algorithms, generalized circulation problem, maximum-flow problem, nodes, graph, linear programming

CITATION

S.A. Plotkin,
E. Tardos,
A.V. Goldberg,
"Combinatorial algorithms for the generalized circulation problem",

*2013 IEEE 54th Annual Symposium on Foundations of Computer Science*, vol. 00, no. , pp. 432-443, 1988, doi:10.1109/SFCS.1988.21959