Approximation schemes for steiner forest on planar graphs and graphs of bounded treewidth
Proceedings of the forty-second ACM symposium on Theory of computing
An improved LP-based approximation for steiner tree
Proceedings of the forty-second ACM symposium on Theory of computing
The prize-collecting edge dominating set problem in trees
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
A primal-dual approximation algorithm for the asymmetric prize-collecting TSP
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Approximation Schemes for Steiner Forest on Planar Graphs and Graphs of Bounded Treewidth
Journal of the ACM (JACM)
Improved Approximation Algorithms for Prize-Collecting Steiner Tree and TSP
SIAM Journal on Computing
Euclidean prize-collecting steiner forest
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Prize-collecting Steiner problems on planar graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Prize-Collecting steiner network problems
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Prize-collecting steiner network problems
ACM Transactions on Algorithms (TALG)
A primal-dual approximation algorithm for the Asymmetric Prize-Collecting TSP
Journal of Combinatorial Optimization
On the approximability of Dense Steiner Problems
Journal of Discrete Algorithms
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We study the prize-collecting versions of the Steiner tree, traveling salesman, and stroll (a.k.a. Path-TSP) problems (PCST, PCTSP, and PCS, respectively): given a graph (V, E) with costs 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 stroll (for PCS) that minimizes the sum of the edge costs in the tree/cycle/stroll 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, giving a 2-approximation algorithm for each, appeared first in 1992. (A 2-approximation for PCS appeared in 2003.) The natural linear programming (LP) 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.