Abstract
In the single-sink buy-at-bulk network design problem we are given a subset of source nodes in a weighted undirected graph: each source node wishes to send a given amount of flow to a sink node. Moreover, a set of cable types is given, each characterized by a cost per unit length and by a capacity: the ratio cost/capacity decreases from small to large cables by economies of scale. The problem is to install cables on edges at minimum cost, such that the flow from each source to the sink can be routed simultaneously. The approximation ratio of this NP-hard problem was gradually reduced from O(log2 n) to 65.49 by a long series of papers. In this paper, we design a better 24.92 approximation algorithm for this problem.
This work has been partially supported by the Sixth Framework Programme of the EU under Contract Number 507613 (Network of Excellence “EuroNGI: Designing and Engineering of the Next Generation Internet”) and by MIUR, under Project ALGO-NEXT.
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References
Awerbuch, B., Azar, Y.: Buy-at-bulk network design. In: IEEE Symposium on Foundations of Computer Science (FOCS), pp. 542–547 (1997)
Bartal, Y.: Probabilistic approximation of metric spaces and its algorithmic applications. In: IEEE Symposium on Foundations of Computer Science (FOCS), pp. 184–193 (1996)
Bartal, Y.: On approximating arbitrary metrics by tree metrics. In: IEEE Symposium on Foundations of Computer Science (FOCS), pp. 161–168 (1998)
Becchetti, L., Konemann, J., Leonardi, S., Pal, M.: Sharing the cost more efficiently: improved approximation for multicommodity rent-or-buy. In: ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 375–384 (2005)
Charikar, M., Chekuri, A., Goel, A., Guha, S.: Approximating a finite metric by a small number of tree metrics. In: IEEE Symposium on Foundations of Computer Science (FOCS), pp. 379–388 (1998)
Eisenbrand, F., Grandoni, F.: An improved approximation algorithm for virtual private network design. In: ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 928–932 (2005)
Eisenbrand, F., Grandoni, F., Oriolo, G., Skutella, M.: New approaches for virtual private network design. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1152–1162. Springer, Heidelberg (2005)
Fakcharoenphol, J., Rao, S., Talwar, K.: A tight bound on approximating arbitrary metrics by tree metrics. In: ACM Symposium on the Theory of Computing (STOC), pp. 448–455 (2003)
Garg, N., Khandekar, R., Konjevod, G., Ravi, R., Salman, F., Sinha, A.: On the integrality gap of a natural formulation of the single-sink buy-at-bulk network design problem. In: Aardal, K., Gerards, B. (eds.) IPCO 2001. LNCS, vol. 2081, pp. 170–184. Springer, Heidelberg (2001)
Guha, S., Meyerson, A., Munagala, K.: A constant factor approximation for the single sink edge installation problem. In: ACM Symposium on the Theory of Computing (STOC), pp. 383–388 (2001)
Gupta, A., Kleinberg, J., Kumar, A., Rastogi, R., Yener, B.: Provisioning a virtual private network: a network design problem for multicommodity flow. In: ACM Symposium on the Theory of Computing (STOC), pp. 389–398 (2001)
Gupta, A., Kumar, A., Pal, M., Roughgarden, T.: Approximation via cost-sharing: simpler and better approximation algorithms for network design (manuscript)
Gupta, A., Kumar, A., Pal, M., Roughgarden, T.: Approximation via cost-sharing: a simple approximation algorithm for the multicommodity rent-or-buy problem. In: IEEE Symposium on Foundations of Computer Science (FOCS), pp. 606–617 (2003)
Gupta, A., Kumar, A., Roughgarden, T.: A constant-factor approximation algorithm for the multicommodity. In: IEEE Symposium on Foundations of Computer Science (FOCS), pp. 333–344 (2002)
Gupta, A., Kumar, A., Roughgarden, T.: Simpler and better approximation algorithms for network design. In: ACM Symposium on the Theory of Computing (STOC), pp. 365–372 (2003)
Jothi, R., Raghavachari, B.: Improved approximation algorithms for the single-sink buy-at-bulk network design problems. In: Hagerup, T., Katajainen, J. (eds.) SWAT 2004. LNCS, vol. 3111, pp. 336–348. Springer, Heidelberg (2004)
Kumar, A., Swamy, C.: Primal-dual algorithms for the connected facility location problem. In: International Workshop on Approximation Algorithms for Combinatorial Optimization, pp. 256–269 (2002)
Meyerson, A., Munagala, K., Plotkin, S.: Cost-distance: two metric network design. In: IEEE Symposium on Foundations of Computer Science (FOCS), pp. 624–630 (2000)
Talwar, K.: The single-sink buy-at-bulk LP has constant integrality gap. In: Cook, W.J., Schulz, A.S. (eds.) IPCO 2002. LNCS, vol. 2337, pp. 475–486. Springer, Heidelberg (2002)
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Grandoni, F., Italiano, G.F. (2006). Improved Approximation for Single-Sink Buy-at-Bulk. In: Asano, T. (eds) Algorithms and Computation. ISAAC 2006. Lecture Notes in Computer Science, vol 4288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11940128_13
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DOI: https://doi.org/10.1007/11940128_13
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