# A Constant Factor Approximation for the Single Sink Edge Installation Problem

## Abstract

*buy-at-bulk*network design problem, where we have to design a network by buying pipes of different costs and capacities per unit length to route demands at a set of sources to a single sink. The distances in the underlying network form a metric. This result improves the previous bound of $O(\log|R|)$, where

*R*is the set of sources. We also present a better constant approximation to the related Access Network Design problem. Our algorithms are randomized and combinatorial. As a subroutine in our algorithm, we use an interesting variant of facility location with lower bounds on the amount of demand an open facility needs to serve. We call this variant

*load balanced facility location*and present a constant factor approximation for it, while relaxing the lower bounds by a constant factor.

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## References

*Hardness of buy-at-bulk network design*, in Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society, Washington, DC, 2004, pp. 115–124.

*The access network design problem*, in Proceedings of the 39th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society, Washington, DC, 1998, pp. 40–49.

*Buy-at-bulk network design*, in Proceedings of the 38th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society, Washington, DC, 1997, pp. 542–47.

*On approximating arbitrary metrics by tree metrics*, in Proceedings of the 30th Annual ACM Symposium on Theory of Computing, ACM, New York, 1998, pp. 161–168.

*Approximating a finite metric by a small number of tree metrics*, in Proceedings of the 39th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society, Washington, DC, 1998.

*On non-uniform multicommodity buy-at-bulk network design*, in Proceedings of the ACM Symposium on Theory of Computing, ACM, New York, 2005, pp. 176–182.

*Approximation algorithms for non-uniform buy-at-bulk network design*, in Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society, Washington, DC, 2006, pp. 677–686.

*On the approximability of network design problems*, in Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms, ACM, New York, SIAM, Philadelphia, 2005, pp. 943–951.

*A tight bound on approximating arbitrary metrics by tree metrics*, in Proceedings of the 35th Annual ACM Symposium on Theory of Computing, ACM, New York, 2003, pp. 448–455.

*On the integrality gap of a natural formulation of the single-sink buy-at-bulk network design problem*, in Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization, Springer-Verlag, London, 2001, pp. 170–184.

*Simultaneous optimization for concave costs: Single sink aggregation or single source buy-at-bulk*, in Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, ACM, New York, SIAM, Philadelphia, 2003, pp. 499–505.

*Hierarchical placement and network design problems*, in Proceedings of the 41st Annual IEEE Symposium on Foundation of Computer Science, IEEE Computer Society, Washington, DC, 2000, pp. 603–612.

*A constant factor approximation for the single sink edge installation problems*, in Proceedings of the 33rd Annual ACM Symposium on Theory of Computing, ACM, New York, 2001, pp. 383–388.

*Generalized clustering*, in Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, ACM, New York, SIAM, Philadelphia, 2002, pp. 484–485.

*Simpler and better approximation algorithms for network design*, in Proceedings of the 35th Annual ACM Symposium on Theory of Computing, ACM, New York, 2003, pp. 365–372.

*Building Steiner trees with incomplete global knowledge*, in Proceedings of the 41st Annual IEEE Syposium of Foundations of Computer Science, IEEE Computer Society, Washington, DC, 2000, pp. 613–623.

*$\epsilon$-approximations with minimum packing constraint violations*, in Proceedings of the 24th Annual ACM Symposium on Theory of Computing, ACM, New York, 1992, pp. 771–782.

*Improved approximation algorithms for metric facility location problems*, in Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization, Spinger-Verlag, London, 2002, pp. 229–242.

*Cost-distance: Two metric network design*, in Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society, Washington, DC, 2000, pp. 624–630.

*Improved Steiner tree approximation in graphs*, in Proceedings of the 11th Annual ACM-SIAM Symposium on Discrete Algorithms, ACM, New York, SIAM, Philadelphia, 2000, pp. 770–779.

*Buy-at-bulk network design: Approximating the single-sink edge installation problem*, in Proceedings of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms, ACM, New York, SIAM, Philadelphia, 1997, pp. 619–628.

*Approximation algorithms for facility location problems*, in Proceedings of the 29th Annual ACM Symposium on Theory of Computing, ACM, New York, 1997, pp. 265–274.

*The single-sink buy-at-bulk LP has constant integrality gap*, in Proceedings of IPCO, Spinger-Verlag, London, 2002, pp. 475–486.

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#### History

**Submitted**: 27 October 2005

**Accepted**: 26 December 2008

**Published online**: 27 March 2009

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