A note on the prize collecting traveling salesman problem
Mathematical Programming: Series A and B
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
A Constant-Factor Approximation Algorithm for the Multicommodity
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
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
FOCS '97 Proceedings of the 38th 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
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
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
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
Survivable network design with degree or order constraints
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Approximating minimum bounded degree spanning trees to within one of optimal
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
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
Elementary approximation algorithms for prize collecting Steiner tree problems
Information Processing Letters
Additive approximation for bounded degree survivable network design
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Additive guarantees for degree bounded directed network design
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Network-design with degree constraints
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Euclidean prize-collecting steiner forest
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
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)
On some network design problems with degree constraints
Journal of Computer and System Sciences
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In this paper we design an iterative rounding approach for the classic prize-collecting Steiner forest problem and more generally the prize-collecting survivable Steiner network design problem. We show as an structural result that in each iteration of our algorithm there is an LP variable in a basic feasible solution which is at least one-third-integral resulting a 3-approximation algorithm for this problem. In addition, we show this factor 3 in our structural result is indeed tight for prize-collecting Steiner forest and thus prize-collecting survivable Steiner network design. This especially answers negatively the previous belief that one might be able to obtain an approximation factor better than 3 for these problems using a natural iterative rounding approach. Our structural result is extending the celebrated iterative rounding approach of Jain [13] by using several new ideas some from more complicated linear algebra. The approach of this paper can be also applied to get a constant factor (bicriteria-)approximation algorithm for degree constrained prize-collecting network design problems. We emphasize that though in theory we can prove existence of only an LP variable of at least one-third-integral, in practice very often in each iteration there exists a variable of integral or almost integral which results in a much better approximation factor than provable factor 3 in this paper (see patent application [11]). This is indeed the advantage of our algorithm in this paper over previous approximation algorithms for prize-collecting Steiner forest with the same or slightly better provable approximation factors.