Approximation via cost sharing: Simpler and better approximation algorithms for network design
Journal of the ACM (JACM)
Approximation algorithms for node-weighted buy-at-bulk network design
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Set connectivity problems in undirected graphs and the directed Steiner network problem
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Stochastic Steiner Tree with Non-uniform Inflation
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Improved approximating algorithms for Directed Steiner Forest
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A constant-factor approximation for stochastic Steiner forest
Proceedings of the forty-first annual ACM symposium on Theory of computing
Approximation Algorithms for Buy-at-Bulk Geometric Network Design
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Approximating Some Network Design Problems with Node Costs
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Competitive cost sharing with economies of scale
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Routing for energy minimization in the speed scaling model
INFOCOM'10 Proceedings of the 29th conference on Information communications
Set connectivity problems in undirected graphs and the directed steiner network problem
ACM Transactions on Algorithms (TALG)
Approximation Algorithms for Nonuniform Buy-at-Bulk Network Design
SIAM Journal on Computing
Oblivious buy-at-bulk in planar graphs
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Approximating k-generalized connectivity via collapsing HSTs
Journal of Combinatorial Optimization
Approximating some network design problems with node costs
Theoretical Computer Science
Approximability of capacitated network design
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Routing for power minimization in the speed scaling model
IEEE/ACM Transactions on Networking (TON)
Approximation algorithms for orienting mixed graphs
Theoretical Computer Science
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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\left( {O\left( {\sqrt {\log h\log \log h} } \right)} \right) for the uniform-demand case, and logD · exp\left( {O\left( {\sqrt {\log h\log \log h} } \right)} \right) 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\left( {\log ^3 h \cdot \min \left\{ {\log D,\gamma \left( {h^2 } \right)} \right\}} \right) where h is the number of pairs and ?(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 \gamma(n) we obtain an O\left( {\min \left\{ {\log ^3 h \cdot \log D,\log ^5 h\log \log h} \right\}} \right) ratio approximation. We also give poly-logarithmic approximations for some variants of the singe-source problem that we need for the multicommodity problem.