Sharing the cost more efficiently

Abstract

In the multicommodity rent-or-buy (MROB) network design problems, we are given a network together with a set of k terminal pairs ( s 1 , t 1 ), …, ( s k , t k . The goal is to provision the network so that a given amount of flow can be shipped between s i and t i for all 1 ≤ i ≤ k simultaneously. In order to provision the network, one can either rent capacity on edges at some cost per unit of flow, or buy them at some larger fixed cost. Bought edges have no incremental, flow-dependent cost. The overall objective is to minimize the total provisioning cost. Recently, Gupta et al. [2003a] presented a 12-approximation for the MROB problem. Their algroithm chooses a subset of the terminal pairs in the graph at random and then buys the edges of an approximate Steiner forest for these pairs. This technique had previously been introduced [Gupta et al. 2003b] for the single-sink rent-or-buy network design problem. In this article we give a 6.828-approximation for the MROB problem by refining the algorithm of Gupta et al. and simplifying their analysis. The improvement in our article is based on a more careful adaptation and simplified analysis of the primal-dual algorithm for the Steiner forest problem due to Agrawal et al. [1995]. Our result significantly reduces the gap between the single-sink and multisink case.