When Trees Collide: An Approximation Algorithm for theGeneralized Steiner Problem on Networks
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A General Approximation Technique for Constrained Forest Problems
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On approximating arbitrary metrices by tree metrics
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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
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The Design of Competitive Online Algorithms via a Primal: Dual Approach
Foundations and Trends® in Theoretical Computer Science
Approximating directed buy-at-bulk network design
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Approximating k-generalized connectivity via collapsing HSTs
Journal of Combinatorial Optimization
Improved approximation algorithms for Directed Steiner Forest
Journal of Computer and System Sciences
Efficient link-heterogeneous multicast for wireless mesh networks
Wireless Networks
Improved bounds on the price of stability in network cost sharing games
Proceedings of the fourteenth ACM conference on Electronic commerce
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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 ⊆ 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, non-metric facility location, tree multicast, and group Steiner tree. Finding a non-trivial approximation ratio for generalized connectivity was left as an open problem. Our starting point is the first polylogarithmic approximation for generalized connectivity attaining 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+ε) approximation, which improves on the currently best performance guarantee of O(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 polylogarithmic approximation; this result improves on the previously known ratio which can be Ω(n) in the worst case.