Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity flows

David Karger, Serge Plotkin
1995 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing - STOC '95  
Minimum cost multicommodity o w is an instance of a simpler problem (multicommodity o w) to which a cost constraint h as been added. In this paper we present a general scheme for solving a large class of such \cost-added" problems|even if more than one cost is added. One o f t h e m ain applications of this method is a new deterministic algorithm for approximately solving t h e minimumcost multicommodity o w problem. Our algorithm nds a (1 + ) a p proximation to t h e minimum cost ow i ñ O ( 3
more » ... mn) t ime, where k is the n u m ber of commodities, m is the n u m ber of edges, and n is the n u m ber vertices in the input problem. This improves the previous best deterministic bounds of O( 4 kmn 2 ) [9] and O( 2 k 2 m 2 ) [15] by factors of n= and km=n respectively. In fact, it even dominates the best randomized bound o f O ( 2 km 2 ) [15] . The algorithm presented in this paper eciently solves several other interesting generalizations of min-cost ow problems, such a s o n e in which each commodity can have its own distinct shipping cost per edge, or one in which t h ere is more than one cost measure on the o ws and all costs must be kept small simultaneously. Our approach is based on an extension of the a p proximate packing techniques in [15] and a generalization of the round-robin approach of [16] to m ulticommodity o w without costs.
doi:10.1145/225058.225073 dblp:conf/stoc/KargerP95 fatcat:oqsreooi3jc6jjo3yq54vjlplm