Approximation Algorithms for Non-Uniform Buy-at-Bulk Network Design

We consider approximation algorithms for non-uniform buy-at-bulk network design problems. The first nontrivial approximation algorithm for this problem is due to Charikar and Karagiozova (STOC’ 05); for an instance on h pairs their algorithm has an approximation guarantee of exp(O( √ log h log log h)) for the uniform-demand case, and log D · exp(O( √ log h log log h)) for the general demand case, where D is the total demand. We improve upon this result, by presenting the first poly-logarithmic approximation for this problem. The ratio we obtain is O(log3 h · min{log D, γ(h2 )}) where h is the number of pairs and γ(n) is the worst case distortion in embedding the metric induced by a n vertex graph into a distribution over its spanning trees. Using the best known upper bound on γ(n) we obtain an O(min{log3 h·log D, log5 h log log h}) ratio approximation. We also give poly-logarithmic approximations for some variants of the singe-source problem that we need for the multicom...

• Type: Conference
• Year: 2006
• Where: FOCS
• Authors: Chandra Chekuri, Mohammad Taghi Hajiaghayi, Guy Kortsarz, Mohammad R. Salavatipour
• Keywords: Approximation Algorithm, Approximations, FOCS 2006, Log H, Theoretical Computer Science