On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Approximation algorithms for directed Steiner problems
Journal of Algorithms
An approximation algorithm for the covering Steiner problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A polylogarithmic approximation algorithm for the group Steiner tree problem
Journal of Algorithms
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for the covering Steiner problem
Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
Integrality ratio for group Steiner trees and directed steiner trees
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
On Network Design Problems: Fixed Cost Flows and the Covering Steiner Problem
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Polylogarithmic inapproximability
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Faster and Simpler Algorithms for Multicommodity Flow and other Fractional Packing Problems.
FOCS '98 Proceedings of the 39th 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
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The Steiner tree problem asks for a minimum cost tree spanning a given set of terminals S ⊆ V in a weighted graph G = (V,E,c), c :E→ R+ In this paper we consider a generalization of the Steiner tree problem, so called Polymatroid Steiner Problem, in which a polymatroid P = P(V) is defined on V and the Steiner tree is required to span at least one base of P (in particular, there may be a single base S ⊆ V) This formulation is motivated by the following application in sensor networks – given a set of sensors S = {s1,...,sk}, each sensor si can choose to monitor only a single target from a subset of targets Xi, find minimum cost tree spanning a set of sensors capable of monitoring the set of all targets X = X1 ∪ .. ∪ Xk The Polymatroid Steiner Problem generalizes many known Steiner tree problem formulations including the group and covering Steiner tree problems We show that this problem can be solved with the polylogarithmic approximation ratio by a generalization of the combinatorial algorithm of Chekuri et al [7]. We also define the Polymatroid directed Steiner problem which asks for a minimum cost arborescence connecting a given root to a base of a polymatroid P defined on the terminal set S We show that this problem can be approximately solved by algorithms generalizing methods of Charikar et al [6].