Abstract
We study two versions of the single sink buy-at-bulk network design problem. We are given a network and a single sink, and several sources which demand a certain amount of flow to be routed to the sink. We are also given a finite set of cable types which have different cost characteristics and obey the principle of economies of scale. We wish to construct a minimum cost network to support the demands, using our given cable types. We study a natural integer program formulation of the problem, and show that its integrality gap is O(k), where k is the number of cable types. As a consequence, we also provide an O(k)-approximation algorithm.
This research was supported by a faculty development grant awarded to R. Ravi by the Carnegie Bosch Institute, Carnegie Mellon University, Pittsburgh PA 15213-3890.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Agrawal, A., Klein, P., Ravi, R.: When trees collide: An approximation algorithm for the generalized Steiner problem on networks. SIAM Journal of Computing, 24(3):440–456, 1995.
Althöfer, I., Das, G., Dobkin, D., Joseph, D., Soares, J.: On sparse spanners of weighted graphs. Discrete and Computational Geometry, 9:81–100, 1993.
Andrews, M., Z hang, L.: The access network design problem. Proc. of the 39th Ann. IEEE Symp. on Foundations of Computer Science, 42–49, October 1998.
Awerbuch, B., Azar, Y.: Buy at bulk network design. Proc. 38th Ann. IEEE Symposium on Foundations of Computer Science, 542–547, 1997.
Bartal, Y.: On approximating arbitrary metrics by tree metrics. Proc. 30th Ann. ACM Symposium on Theory of Computing, 1998.
Garg, N., Khandekar, R., Konjevod, G., Ravi, R., Salman, F.S., Sinha, A.: A mathematical formulation of a transportation problem with economies of scale. Carnegie Bosch Institute Working Paper 01–1, 2001.
Guha, S., M eyerson, A., Munagala, K.: Improved combinatorial algorithms for single sink edge installation problems. To appear in Proc. 33rd Ann. ACM Symposium on Theory of Computing, 2001.
Guha, S., Meyerson, A., Munagala, K.: Heirarchical placement and network design problems. Proc. 41st Ann. IEEE Symposium on Foundations of Computer Sciece, 2000.
Hassin, R., R avi, R., Salman, F.S.: Approximation algorithms for a capacitated network design problem. Proc. of the APPROX 2000, 167–176, 2000.
Khuller, S., Raghavachari, B., Young, N.E.: Balancing minimum spanning and shortest path trees. Algorithmica, 14, 305–322, 1993.
Mansour, Y., P eleg, D.: An approximation algorithm for minimum-cost network design. The Weizman Institute of Science, Rehovot, 76100 Israel, Tech. Report CS94-22, 1994; Also presented at the DIMACS workshop on Robust Communication Networks, 1998.
Meyerson, A., Munagala, K., Plotkin, S.: Cost-distance: Two metric network design. Proc. 41st Ann. IEEE Symposium on Foundations of Computer Science, 2000.
Ravi, R., Salman, F.S.: Approximation algorithms for the traveling purchaser problem and its variants in network design. Proc. of the European Symposium on Algorithms, 29–40, 1999.
Salman, F.S., Cheriyan, J., Ravi R., Subramanian, S.: Approximating the single sink link-installation problem in network design. SIAM Journal of Optimization 11(3):595–610, 2000.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Garg, N., Khandekar, R., Konjevod, G., Ravi, R., Salman, F.S., Sinha, A. (2001). On the Integrality Gap of a Natural Formulation of the Single-sink Buy-at-Bulk Network Design Problem. In: Aardal, K., Gerards, B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2001. Lecture Notes in Computer Science, vol 2081. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45535-3_14
Download citation
DOI: https://doi.org/10.1007/3-540-45535-3_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42225-9
Online ISBN: 978-3-540-45535-6
eBook Packages: Springer Book Archive