When Trees Collide: An Approximation Algorithm for theGeneralized Steiner Problem on Networks
SIAM Journal on Computing
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
A nearly best-possible approximation algorithm for node-weighted Steiner trees
Journal of Algorithms
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Bicriteria network design problems
Journal of Algorithms
Efficient recovery from power outage (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
A deterministic algorithm for the cost-distance problem
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms
Approximating the Single-Sink Link-Installation Problem in Network Design
SIAM Journal on Optimization
A Constant-Factor Approximation Algorithm for the Multicommodity
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
The Single-Sink Buy-at-Bulk LP Has Constant Integrality Gap
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Simpler and better approximation algorithms for network design
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Hardness of Buy-at-Bulk Network Design
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
A tight bound on approximating arbitrary metrics by tree metrics
Journal of Computer and System Sciences - Special issue: STOC 2003
On non-uniform multicommodity buy-at-bulk network design
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Tighter Bounds for Graph Steiner Tree Approximation
SIAM Journal on Discrete Mathematics
The prize-collecting generalized steiner tree problem via a new approach of primal-dual schema
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Iterative rounding 2-approximation algorithms for minimum-cost vertex connectivity problems
Journal of Computer and System Sciences - Special issue on FOCS 2001
Approximation Algorithms for Non-Uniform Buy-at-Bulk Network Design
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
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
On the approximability of some network design problems
ACM Transactions on Algorithms (TALG)
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
Cost-Distance: Two Metric Network Design
SIAM Journal on Computing
A Constant Factor Approximation for the Single Sink Edge Installation Problem
SIAM Journal on Computing
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
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Buy-at-bulk network design problems arise in settings where the costs for purchasing or installing equipment exhibit economies of scale. The objective is to build a network of cheapest cost to support a given multicommodity flow demand between node pairs. We present approximation algorithms for buy-at-bulk network design problems with costs on both edges and nodes of an undirected graph. Our main result is the first poly-logarithmic approximation ratio for the non-uniform problem that allows different cost functions on each edge and node; the ratio we achieve is $O(\log^4 h)$, where $h$ is the number of demand pairs. In addition we present an $O(\log h)$ approximation for the single sink problem. Poly-logarithmic ratios for some related problems are also obtained. Our algorithm for the multicommodity problem is obtained via a reduction to the single source problem using the notion of junction trees. We believe that this presents a simple yet useful general technique for network design problems.