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

dc.contributor.author | Goel, Ashish | |

dc.contributor.author | Post, Ian | |

dc.contributor.institution | Stanford University, Palo Alto, United States | |

dc.date.accessioned | 2016-02-25T12:41:41Z | |

dc.date.available | 2016-02-25T12:41:41Z | |

dc.date.issued | 2009-10 | |

dc.description.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. | |

dc.description.sponsorship | Research supported by an NSF ITR grant and the Stanford-KAUSTalliance for academic excellence. | |

dc.identifier.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. | |

dc.identifier.doi | 10.1109/FOCS.2009.41 | |

dc.identifier.journal | 2009 50th Annual IEEE Symposium on Foundations of Computer Science | |

dc.identifier.uri | http://hdl.handle.net/10754/597539 | |

dc.publisher | Institute of Electrical and Electronics Engineers (IEEE) | |

dc.title | An Oblivious O(1)-Approximation for Single Source Buy-at-Bulk | |

dc.type | Conference Paper | |

display.details.left | <span><h5>Type</h5>Conference Paper<br><br><h5>Authors</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Goel, Ashish,equals">Goel, Ashish</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Post, Ian,equals">Post, Ian</a><br><br><h5>Date</h5>2009-10</span> | |

display.details.right | <span><h5>Abstract</h5>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.<br><br><h5>Citation</h5>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.<br><br><h5>Acknowledgements</h5>Research supported by an NSF ITR grant and the Stanford-KAUSTalliance for academic excellence.<br><br><h5>Publisher</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.publisher=Institute of Electrical and Electronics Engineers (IEEE),equals">Institute of Electrical and Electronics Engineers (IEEE)</a><br><br><h5>Journal</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.journal=2009 50th Annual IEEE Symposium on Foundations of Computer Science,equals">2009 50th Annual IEEE Symposium on Foundations of Computer Science</a><br><br><h5>DOI</h5><a href="https://doi.org/10.1109/FOCS.2009.41">10.1109/FOCS.2009.41</a></span> | |

orcid.author | Goel, Ashish | |

orcid.author | Post, Ian |