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Anupam Gupta, Amit Kumar, Martin Pál, Tim Roughgarden, "Approximation Via CostSharing: A Simple Approximation Algorithm for the Multicommodity RentorBuy Problem," 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 606, 44th Annual IEEE Symposium on Foundations of Computer Science (FOCS'03), 2003.  
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@article{ 10.1109/SFCS.2003.1238233, author = {Anupam Gupta and Amit Kumar and Martin Pál and Tim Roughgarden}, title = {Approximation Via CostSharing: A Simple Approximation Algorithm for the Multicommodity RentorBuy Problem}, journal ={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, volume = {0}, year = {2003}, issn = {02725428}, pages = {606}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.2003.1238233}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  CONF JO  2013 IEEE 54th Annual Symposium on Foundations of Computer Science TI  Approximation Via CostSharing: A Simple Approximation Algorithm for the Multicommodity RentorBuy Problem SN  02725428 SP EP A1  Anupam Gupta, A1  Amit Kumar, A1  Martin Pál, A1  Tim Roughgarden, PY  2003 KW  null VL  0 JA  2013 IEEE 54th Annual Symposium on Foundations of Computer Science ER   
We study the multicommodity rentorbuy 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 perunit of capacity basis, or bought, which allows unlimited use after payment of a large fixed cost. Given a graph and a set of sourcesink pairs, we seek a minimumcost 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 constantfactor 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 12approximation 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.