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44th Annual IEEE Symposium on Foundations of Computer Science (FOCS'03)
Approximation Via Cost-Sharing: A Simple Approximation Algorithm for the Multicommodity Rent-or-Buy Problem
Cambridge, Massachusettes
October 11-October 14
ISBN: 0-7695-2040-5
Anupam Gupta, Carnegie Mellon University
Amit Kumar, Lucent Bell Labs
Martin Pál, Cornell University
Tim Roughgarden, Cornell University

We study the multicommodity rent-or-buy problem, a type of network design problem with economies of scale. In this problem, capacity on an edge can be rented, with cost incurred on a per-unit of capacity basis, or bought, which allows unlimited use after payment of a large fixed cost. Given a graph and a set of source-sink pairs, we seek a minimum-cost way of installing sufficient capacity on edges so that a prescribed amount of flow can be sent simultaneously from each source to the corresponding sink. The first constant-factor approximation algorithm for this problem was recently given by Kumar et al. (FOCS ?02); however, this algorithm and its analysis are both quite complicated, and its performance guarantee is extremely large.

In this paper, we give a conceptually simple 12-approximation algorithm for this problem. Our analysis of this algorithm makes crucial use of cost sharing, the task of allocating the cost of an object to many users of the object in a "fair" manner. While techniques from approximation algorithms have recently yielded new progress on cost sharing problems, our work is the first to show the converse — that ideas from cost sharing can be fruitfully applied in the design and analysis of approximation algorithms.

Citation:
Anupam Gupta, Amit Kumar, Martin Pál, Tim Roughgarden, "Approximation Via Cost-Sharing: A Simple Approximation Algorithm for the Multicommodity Rent-or-Buy Problem," focs, pp.606, 44th Annual IEEE Symposium on Foundations of Computer Science (FOCS'03), 2003
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