Hardness of buy-at-bulk network design

We consider the buy-at-bulk network design problem in which we wish to design a network for carrying multicommodity demands from a set of source nodes to a set of destination nodes. The key feature of the problem is that the cost of capacity on each edge is concave and hence exhibits economies of scale. If the cost of capacity per unit length can be different on different edges then, we say that the problem is non-uniform. The problem is uniform otherwise. We show that for any constant /spl gamma/, if NP /spl nsube/ ZPTIME(n/sup polylog n/), then there is no O(log/sup 1/2 - /spl gamma//N)-approximation algorithm for non-uniform buy-at-bulk network design and there is no O(log/sup 1/4 - /spl gamma//N)-approximation algorithm for the uniform problem.

[1]  Yair Bartal,et al.  On approximating arbitrary metrices by tree metrics , 1998, STOC '98.

[2]  H. Sachs,et al.  Regukre Graphen gegebener Taillenweite mit minimaler Knotenzahl , 1963 .

[3]  Joseph Naor,et al.  A deterministic algorithm for the cost-distance problem , 2001, SODA '01.

[4]  Lisa Zhang,et al.  Bounds on fiber minimization in optical networks with fixed fiber capacity , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[5]  Tim Roughgarden,et al.  Simpler and better approximation algorithms for network design , 2003, STOC '03.

[6]  Lisa Zhang,et al.  The access network design problem , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

[7]  Felix Lazebnik,et al.  Explicit Construction of Graphs with an Arbitrary Large Girth and of Large Size , 1995, Discret. Appl. Math..

[8]  Tim Roughgarden,et al.  A constant-factor approximation algorithm for the multicommodity rent-or-buy problem , 2002, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings..

[9]  Kamesh Munagala,et al.  Cost-distance: two metric network design , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[10]  Yossi Azar,et al.  Buy-at-bulk network design , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[11]  R. Ravi,et al.  Buy-at-bulk network design: approximating the single-sink edge installation problem , 1997, SODA '97.

[12]  Deborah Estrin,et al.  Simultaneous Optimization for Concave Costs: Single Sink Aggregation or Single Source Buy-at-Bulk , 2003, SODA '03.

[13]  Sanjeev Khanna,et al.  Design networks with bounded pairwise distance , 1999, STOC '99.

[14]  Guy Kortsarz.  On the Hardness of Approximating Spanners , 2001, Algorithmica.

[15]  Sudipto Guha,et al.  Hierarchical placement and network design problems , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[16]  Sudipto Guha,et al.  A constant factor approximation for the single sink edge installation problems , 2001, STOC '01.

[17]  Satish Rao,et al.  A tight bound on approximating arbitrary metrics by tree metrics , 2003, STOC '03.

[18]  Tim Roughgarden,et al.  Approximation via cost-sharing: a simple approximation algorithm for the multicommodity rent-or-buy problem , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[19]  Jacques Stern,et al.  The hardness of approximate optima in lattices, codes, and systems of linear equations , 1993, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.

[20]  DistanceYevgeniy Dodis,et al.  Designing Networks with Bounded Pairwise Distance , 1999 .

[21]  Ran Raz,et al.  A parallel repetition theorem , 1995, STOC '95.