A double scaling algorithm for the constrained maximum flow problem

Authors:
Cenk Çalışkan
Affiliations:
Department of Business Administration, Alfred Lerner College of Business and Economics, University of Delaware, Newark, DE 19716, USA
Venue:
Computers and Operations Research
Year:
2008

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Abstract

The constrained maximum flow problem is to send the maximum possible flow from a source node to a sink node in a directed capacitated network subject to a budget constraint that the total cost of the flow can be at most D. In this research, we present a double scaling algorithm whose generic version runs in time, where n is the number of nodes in the network; m, the number of arcs; C, the largest arc cost; and U, the largest arc capacity. This running time can be further reduced to with the wave implementation of the cost scaling algorithm, and to O(nmlog(n2/m)logmlog Ulog(nC)) with the use of dynamic trees. These bounds are better than the current bound of , where S(n,m,nC) is the time to find a shortest path from a single source to all other nodes where nonnegative reduced costs are used as arc costs.