An Oblivious O(1)-Approximation for Single Source Buy-at-Bulk

Handle URI:
http://hdl.handle.net/10754/597539
Title:
An Oblivious O(1)-Approximation for Single Source Buy-at-Bulk
Authors:
Goel, Ashish; Post, Ian
Abstract:
We consider the single-source (or single-sink) buy-at-bulk problem with an unknown concave cost function. We want to route a set of demands along a graph to or from a designated root node, and the cost of routing x units of flow along an edge is proportional to some concave, non-decreasing function f such that f(0) = 0. We present a polynomial time algorithm that finds a distribution over trees such that the expected cost of a tree for any f is within an O(1)-factor of the optimum cost for that f. The previous best simultaneous approximation for this problem, even ignoring computation time, was O(log |D|), where D is the multi-set of demand nodes. We design a simple algorithmic framework using the ellipsoid method that finds an O(1)-approximation if one exists, and then construct a separation oracle using a novel adaptation of the Guha, Meyerson, and Munagala [10] algorithm for the single-sink buy-at-bulk problem that proves an O(1) approximation is possible for all f. The number of trees in the support of the distribution constructed by our algorithm is at most 1 + log |D|. © 2009 IEEE.
Citation:
Goel A, Post I (2009) An Oblivious O(1)-Approximation for Single Source Buy-at-Bulk. 2009 50th Annual IEEE Symposium on Foundations of Computer Science. Available: http://dx.doi.org/10.1109/FOCS.2009.41.
Publisher:
Institute of Electrical and Electronics Engineers (IEEE)
Journal:
2009 50th Annual IEEE Symposium on Foundations of Computer Science
Issue Date:
Oct-2009
DOI:
10.1109/FOCS.2009.41
Type:
Conference Paper
Sponsors:
Research supported by an NSF ITR grant and the Stanford-KAUSTalliance for academic excellence.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorGoel, Ashishen
dc.contributor.authorPost, Ianen
dc.date.accessioned2016-02-25T12:41:41Zen
dc.date.available2016-02-25T12:41:41Zen
dc.date.issued2009-10en
dc.identifier.citationGoel A, Post I (2009) An Oblivious O(1)-Approximation for Single Source Buy-at-Bulk. 2009 50th Annual IEEE Symposium on Foundations of Computer Science. Available: http://dx.doi.org/10.1109/FOCS.2009.41.en
dc.identifier.doi10.1109/FOCS.2009.41en
dc.identifier.urihttp://hdl.handle.net/10754/597539en
dc.description.abstractWe consider the single-source (or single-sink) buy-at-bulk problem with an unknown concave cost function. We want to route a set of demands along a graph to or from a designated root node, and the cost of routing x units of flow along an edge is proportional to some concave, non-decreasing function f such that f(0) = 0. We present a polynomial time algorithm that finds a distribution over trees such that the expected cost of a tree for any f is within an O(1)-factor of the optimum cost for that f. The previous best simultaneous approximation for this problem, even ignoring computation time, was O(log |D|), where D is the multi-set of demand nodes. We design a simple algorithmic framework using the ellipsoid method that finds an O(1)-approximation if one exists, and then construct a separation oracle using a novel adaptation of the Guha, Meyerson, and Munagala [10] algorithm for the single-sink buy-at-bulk problem that proves an O(1) approximation is possible for all f. The number of trees in the support of the distribution constructed by our algorithm is at most 1 + log |D|. © 2009 IEEE.en
dc.description.sponsorshipResearch supported by an NSF ITR grant and the Stanford-KAUSTalliance for academic excellence.en
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.titleAn Oblivious O(1)-Approximation for Single Source Buy-at-Bulken
dc.typeConference Paperen
dc.identifier.journal2009 50th Annual IEEE Symposium on Foundations of Computer Scienceen
dc.contributor.institutionStanford University, Palo Alto, United Statesen
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