The steiner problem with edge lengths 1 and 2,
Information Processing Letters
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
The prize collecting Steiner tree problem: theory and practice
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Approximating the Single-Sink Link-Installation Problem in Network Design
SIAM Journal on Optimization
Approximate k-MSTs and k-Steiner Trees via the Primal-Dual Method and Lagrangean Relaxation
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
An Iterative Rounding 2-Approximation Algorithm for the Element Connectivity Problem
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Tighter Bounds for Graph Steiner Tree Approximation
SIAM Journal on Discrete Mathematics
The prize-collecting generalized steiner tree problem via a new approach of primal-dual schema
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
An efficient cost-sharing mechanism for the prize-collecting Steiner forest problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for prize collecting forest problems with submodular penalty functions
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Combinatorial Optimization: Theory and Algorithms
Combinatorial Optimization: Theory and Algorithms
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 O(k^3 log n)-Approximation Algorithm for Vertex-Connectivity Survivable Network Design
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
Prize-collecting steiner networks via iterative rounding
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
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In the Steiner Network problem, we are given a graph G with edge-costs and connectivity requirements ruv between node pairs u,v. The goal is to find a minimum-cost subgraph H of G that contains ruv edge-disjoint paths for all u,v ∈ V. In Prize-Collecting Steiner Network problems, we do not need to satisfy all requirements, but are given a penalty function for violating the connectivity requirements, and the goal is to find a subgraph H that minimizes the cost plus the penalty. The case when ruv ∈ {0,1} is the classic Prize-Collecting Steiner Forest problem. In this article, we present a novel linear programming relaxation for the Prize-Collecting Steiner Network problem, and by rounding it, obtain the first constant-factor approximation algorithm for submodular and monotone nondecreasing penalty functions. In particular, our setting includes all-or-nothing penalty functions, which charge the penalty even if the connectivity requirement is slightly violated; this resolves an open question posed by Nagarajan et al. [2008]. We further generalize our results for element-connectivity and node-connectivity.