Abstract
In the oblivious buy-at-bulk network design problem in a graph, the task is to compute a fixed set of paths for every pair of source-destination in the graph, such that any set of demands can be routed along these paths. The demands could be aggregated at intermediate edges where the fusion-cost is specified by a canonical (non-negative concave) function f. We give a novel algorithm for planar graphs which is oblivious with respect to the demands, and is also oblivious with respect to the fusion function f. The algorithm is deterministic and computes the fixed set of paths in polynomial time, and guarantees a O(logn) approximation ratio for any set of demands and any canonical fusion function f, where n is the number of nodes. The algorithm is asymptotically optimal, since it is known that this problem cannot be approximated with better than Ω(logn) ratio. To our knowledge, this is the first tight analysis for planar graphs, and improves the approximation ratio by a factor of logn with respect to previously known results.
This work is supported by NSF grant CNS-084608.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Awerbuch, B., Azar, Y.: Buy-at-bulk network design. In: FOCS 1997, Washington, DC, USA, p. 542. IEEE Computer Society, Los Alamitos (1997)
Bartal, Y.: Competitive analysis of distributed online problems - distributed paging. Ph.D. Dissertation (1994)
Bartal, Y.: On approximating arbitrary metrices by tree metrics. In: STOC 1998, pp. 161–168. ACM, New York (1998)
Busch, C., LaFortune, R., Tirthapura, S.: Improved sparse covers for graphs excluding a fixed minor. In: PODC 2007: Proceedings of the Twenty-sixth Annual ACM Symposium on Principles of Distributed Computing, pp. 61–70. ACM, New York (2007)
Chekuri, C., Hajiaghayi, M.T., Kortsarz, G., Salavatipour, M.R.: Approximation algorithms for non-uniform buy-at-bulk network design. In: FOCS 2006, Washington, DC, USA, pp. 677–686 (2006)
Goel, A., Estrin, D.: Simultaneous optimization for concave costs: single sink aggregation or single source buy-at-bulk. In: SODA 2003, pp. 499–505. SIAM, Philadelphia (2003)
Goel, A., Post, I.: An oblivious o(1)-approximation for single source buy-at-bulk. In: Annual IEEE Symposium on Foundations of Computer Science, pp. 442–450 (2009)
Goel, A., Post, I.: One tree suffices: A simultaneous o(1)-approximation for single-sink buy-at-bulk. In: Annual IEEE Symposium on Foundations of Computer Science (2010)
Grandoni, F., Rothvoß, T.: Network design via core detouring for problems without a core. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6198, pp. 490–502. Springer, Heidelberg (2010)
Guha, S., Meyerson, A., Munagala, K.: A constant factor approximation for the single sink edge installation problems. In: STOC 2001, pp. 383–388. ACM, New York (2001)
Gupta, A., Hajiaghayi, M.T., Räcke, H.: Oblivious network design. In: SODA 2006: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithm, New York, NY, USA, pp. 970–979 (2006)
Imase, M., Waxman, B.M.: Dynamic steiner tree problem. SIAM Journal on Discrete Mathematics 4(3), 369–384 (1991)
Jia, L., Lin, G., Noubir, G., Rajaraman, R., Sundaram, R.: Universal approximations for tsp, steiner tree, and set cover. In: STOC 2005: Proceedings of the Thirty-seventh Annual ACM Symposium on Theory of Computing, pp. 386–395. ACM, New York (2005)
Jia, L., Noubir, G., Rajaraman, R., Sundaram, R.: GIST: Group-independent spanning tree for data aggregation in dense sensor networks. In: Gibbons, P.B., Abdelzaher, T., Aspnes, J., Rao, R. (eds.) DCOSS 2006. LNCS, vol. 4026, pp. 282–304. Springer, Heidelberg (2006)
Mansour, Y., Peleg, D.: An approximation algorithm for minimum-cost network design. Technical report, Jerusalem, Israel, Israel (1994)
Peleg, D.: Distributed computing: a locality-sensitive approach. SIAM, Philadelphia (2000)
Salman, F.S., Cheriyan, J., Ravi, R., Subramanian, S.: Approximating the single-sink link-installation problem in network design. SIAM J. on Optimization 11(3), 595–610 (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. 475–480. Springer, Heidelberg (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Srinivasagopalan, S., Busch, C., Iyengar, S.S. (2011). Oblivious Buy-at-Bulk in Planar Graphs. In: Katoh, N., Kumar, A. (eds) WALCOM: Algorithms and Computation. WALCOM 2011. Lecture Notes in Computer Science, vol 6552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19094-0_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-19094-0_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-19093-3
Online ISBN: 978-3-642-19094-0
eBook Packages: Computer ScienceComputer Science (R0)