A general approximation technique for constrained forest problems
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Improved approximations for the Steiner tree problem
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
A note on the prize collecting traveling salesman problem
Mathematical Programming: Series A and B
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 2.5-factor approximation algorithm for the k-MST problem
Information Processing Letters
A 1.598 approximation algorithm for the Steiner problem in graphs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
The prize collecting Steiner tree problem: theory and practice
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Improved Steiner tree approximation in graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
RNC-Approximation Algorithms for the Steiner Problem
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
The Dynamic Vertex Minimum Problem and Its Application to Clustering-Type Approximation Algorithms
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
A 3-approximation for the minimum tree spanning k vertices
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Better approximation bounds for the network and Euclidean Steiner tree problems
Better approximation bounds for the network and Euclidean Steiner tree problems
Paths, Trees, and Minimum Latency Tours
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Approximate k-MSTs and k-Steiner trees via the primal-dual method and Lagrangean relaxation
Mathematical Programming: Series A and B
Saving an epsilon: a 2-approximation for the k-MST problem in graphs
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Improved Combinatorial Algorithms for Facility Location Problems
SIAM Journal on Computing
Network design for information networks
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Tighter Bounds for Graph Steiner Tree Approximation
SIAM Journal on Discrete Mathematics
A 2 + ɛ approximation algorithm for the k-MST problem
Mathematical Programming: Series A and B
A Faster, Better Approximation Algorithm for the Minimum Latency Problem
SIAM Journal on Computing
Improved Approximation Algorithms for PRIZE-COLLECTING STEINER TREE and TSP
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
An improved LP-based approximation for steiner tree
Proceedings of the forty-second ACM symposium on Theory of computing
Improved approximation algorithms for the minimum latency problem via prize-collecting strolls
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Improving christofides' algorithm for the s-t path TSP
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Steiner Tree Approximation via Iterative Randomized Rounding
Journal of the ACM (JACM)
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We study the prize-collecting Steiner tree (PCST), prize-collecting traveling salesman (PCTSP), and prize-collecting path (PC-Path) problems. Given a graph $(V,E)$ with a cost on each edge and a penalty (a.k.a. prize) on each node, the goal is to find a tree (for PCST), cycle (for PCTSP), or path (for PC-Path) that minimizes the sum of the edge costs in the tree/cycle/path and the penalties of the nodes not spanned by it. In addition to being a useful theoretical tool for helping to solve other optimization problems, PCST has been applied fruitfully by AT&T to the optimization of real-world telecommunications networks. The most recent improvements for the first two problems, a 2-approximation algorithm for each, appeared first in 1992; a 2-approximation for PC-Path appeared in 2003. The natural linear programming relaxation of PCST has an integrality gap of 2, which has been a barrier to further improvements for this problem. We present $(2-\epsilon)$-approximation algorithms for all three problems, connected by a unified technique for improving prize-collecting algorithms that allows us to circumvent the integrality gap barrier. Specifically, our approximation ratio for prize-collecting Steiner tree is below 1.9672.