When Trees Collide: An Approximation Algorithm for theGeneralized Steiner Problem on Networks
SIAM Journal on Computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Greedy strikes back: improved facility location algorithms
Journal of Algorithms
Provisioning a virtual private network: a network design problem for multicommodity flow
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
A Constant-Factor Approximation Algorithm for the Multicommodity
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
The Single-Sink Buy-at-Bulk LP Has Constant Integrality Gap
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Cost-distance: two metric network design
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Building Steiner trees with incomplete global knowledge
FOCS '00 Proceedings of the 41st 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
Sharing the cost more efficiently: improved approximation for multicommodity rent-or-buy
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
An improved approximation algorithm for virtual private network design
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Simple cost sharing schemes for multicommodity rent-or-buy and stochastic Steiner tree
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Approximation via cost sharing: Simpler and better approximation algorithms for network design
Journal of the ACM (JACM)
New Approaches for Virtual Private Network Design
SIAM Journal on Computing
The Steiner tree problem on graphs: Inapproximability results
Theoretical Computer Science
An Optimal Bifactor Approximation Algorithm for the Metric Uncapacitated Facility Location Problem
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
A constant-factor approximation for stochastic Steiner forest
Proceedings of the forty-first annual ACM symposium on Theory of computing
On the Complexity of the Asymmetric VPN Problem
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
A Constant Factor Approximation for the Single Sink Edge Installation Problem
SIAM Journal on Computing
An improved LP-based approximation for steiner tree
Proceedings of the forty-second ACM symposium on Theory of computing
Connected facility location via random facility sampling and core detouring
Journal of Computer and System Sciences
Network design via core detouring for problems without a core
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Improved approximation for single-sink buy-at-bulk
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Steiner Tree Approximation via Iterative Randomized Rounding
Journal of the ACM (JACM)
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In the classical facility location problem we are given a set of facilities, with associated opening costs, and a set of clients. The goal is to open a subset of facilities, and to connect each client to the closest open facility, so that the total connection and opening cost is minimized. In some applications, however, open facilities need to be connected via an infrastructure. Furthermore, connecting two facilities among them is typically more expensive than connecting a client to a facility (for a given path length). This scenario motivated the study of the connected facility location problem (CFL). Here we are also given a parameter M ≥ 1. A feasible solution consists of a subset of open facilities and a Steiner tree connecting them. The cost of the solution is now the opening cost, plus the connection cost, plus M times the cost of the Steiner tree. In this paper we investigate the approximability of CFL and related problems. More precisely, we achieve the following results: • We present a new, simple 3.19 approximation algorithm for CFL. The previous best approximation factor is 3.92 [Eisenbrand, Grandoni, Rothvoß, Schäfer-'10]. • We show that SROB, i.e. the special case of CFL where all opening costs are 0, is hard to approximate within 1.28. The previous best lower bound for SROB is 1.01, and derives trivially from Steiner tree inapproximability [Chlebík, Chlebíková-'08]. The same inapproximability result extends to other well-studied problems, such as virtual private network and single-sink buy-at-bulk. • We introduce and study a natural multi-commodity generalization MCFL of CFL. In MCFL we are given source-sink pairs (rather than clients) that we wish to connect. A feasible solution consists of a subset of open facilities, and a forest (rather than a tree) spanning them. Source-sink connection paths can use several trees in the forest, but must enter and leave each tree at open facilities. We present the first constant approximation for MCFL.