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
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
The primal-dual method for approximation algorithms and its application to network design problems
Approximation algorithms for NP-hard problems
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Design networks with bounded pairwise distance
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Approximation algorithms for directed Steiner problems
Journal of Algorithms
A polylogarithmic approximation algorithm for the group Steiner tree problem
Journal of Algorithms
Approximation algorithms
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Polylogarithmic inapproximability
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual 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
Approximation Algorithms for Non-Uniform Buy-at-Bulk Network Design
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
A general approach to online network optimization problems
ACM Transactions on Algorithms (TALG)
Integrality Ratio for Group Steiner Trees and Directed Steiner Trees
SIAM Journal on Computing
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SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
The Set Connector Problem in Graphs
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Approximating buy-at-bulk and shallow-light k-Steiner trees
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Approximation algorithms for spanner problems and Directed Steiner Forest
Information and Computation
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Theoretical Computer Science
The subdivision-constrained routing requests problem
Journal of Combinatorial Optimization
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In the generalized connectivity problem, we are given an edge-weighted graph G = (V,E) and a collection D = {(S1, T1), …, (Sk, Tk)} of distinct demands each demand (Si,Ti) is a pair of disjoint vertex subsets. We say that a subgraph F of G connects a demand (Si, Ti) when it contains a path with one endpoint in Si and the other in Ti. The goal is to identify a minimum weight subgraph that connects all demands in D. Alon et al. (SODA '04) introduced this problem to study online network formation settings and showed that it captures some well-studied problems such as Steiner forest, facility location with nonmetric costs, tree multicast, and group Steiner tree. Obtaining a nontrivial approximation ratio for generalized connectivity was left as an open problem. We describe the first poly-logarithmic approximation algorithm for generalized connectivity that has a performance guarantee of O(log2 n log2 k). Here, n is the number of vertices in G and k is the number of demands. We also prove that the cut-covering relaxation of this problem has an O(log3 n log2 k) integrality gap. Building upon the results for generalized connectivity, we obtain improved approximation algorithms for two problems that contain generalized connectivity as a special case. For the directed Steiner network problem, we obtain an O(k1/2 + &epsis;) approximation which improves on the currently best performance guarantee of Õ(k2/3) due to Charikar et al. (SODA '98). For the set connector problem, recently introduced by Fukunaga and Nagamochi (IPCO '07), we present a poly-logarithmic approximation; this result improves on the previously known ratio which can be Ω(n) in the worst case.