Theory of linear and integer programming
Theory of linear and integer programming
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
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Efficient recovery from power outage (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Applications of approximation algorithms to cooperative games
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximation algorithms for constrained for constrained node weighted steiner tree problems
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Equitable cost allocations via primal-dual-type algorithms
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Relations between average case complexity and approximation complexity
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
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
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
Strategyproof cost-sharing mechanisms for set cover and facility location games
Proceedings of the 4th ACM conference on Electronic commerce
Simpler and better approximation algorithms for network design
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
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
Group Strategyproof Mechanisms via Primal-Dual Algorithms
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Ruling Out PTAS for Graph Min-Bisection, Densest Subgraph and Bipartite Clique
FOCS '04 Proceedings of the 45th 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
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximate k-Steiner forests via the Lagrangian relaxation technique with internal preprocessing
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
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
Approximating Generalized Multicut on Trees
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Bicriteria Approximation Tradeoff for the Node-Cost Budget Problem
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Elementary Approximation Algorithms for Prize Collecting Steiner Tree Problems
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Improved approximating algorithms for Directed Steiner Forest
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Bicriteria approximation tradeoff for the node-cost budget problem
ACM Transactions on Algorithms (TALG)
Approximation and Online Algorithms
An approximation algorithm to the k-Steiner Forest problem
Theoretical Computer Science
Node-Weighted Steiner Tree and Group Steiner Tree in Planar Graphs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
ACM Transactions on Algorithms (TALG)
An approximation algorithm to the k-Steiner forest problem
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Approximation Algorithms for Nonuniform Buy-at-Bulk Network Design
SIAM Journal on Computing
Approximating k-generalized connectivity via collapsing HSTs
Journal of Combinatorial Optimization
Improved approximation algorithms for Directed Steiner Forest
Journal of Computer and System Sciences
Euclidean prize-collecting steiner forest
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Prize-collecting steiner networks via iterative rounding
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
Approximating buy-at-bulk and shallow-light k-Steiner trees
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
An approximation algorithm for the Generalized k-Multicut problem
Discrete Applied Mathematics
Prize-Collecting steiner network problems
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
A note on the subadditive network design problem
Operations Research Letters
Prize-collecting steiner network problems
ACM Transactions on Algorithms (TALG)
On the k-edge-incident subgraph problem and its variants
Discrete Applied Mathematics
A new approximation algorithm for the Selective Single-Sink Buy-at-Bulk problem in network design
Journal of Combinatorial Optimization
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In this paper we study the prize-collecting version of the Generalized Steiner Tree problem. To the best of our knowledge, there is no general combinatorial technique in approximation algorithms developed to study the prize-collecting versions of various problems. These problems are studied on a case by case basis by Bienstock et al. [5] by applying an LP-rounding technique which is not a combinatorial approach. The main contribution of this paper is to introduce a general combinatorial approach towards solving these problems through novel primal-dual schema (without any need to solve an LP). We fuse the primal-dual schema with Farkas lemma to obtain a combinatorial 3-approximation algorithm for the Prize-Collecting Generalized Steiner Tree problem. Our work also inspires a combinatorial algorithm [19] for solving a special case of Kelly's problem [22] of pricing edges.We also consider the k-forest problem, a generalization of k-MST and k-Steiner tree, and we show that in spite of these problems for which there are constant factor approximation algorithms, the k-forest problem is much harder to approximate. In particular, obtaining an approximation factor better than O(n1/6-ε) for k-forest requires substantially new ideas including improving the approximation factor O(n1/3-ε) for the notorious densest k-subgraph problem. We note that k-forest and prize-collecting version of Generalized Steiner Tree are closely related to each other, since the latter is the Lagrangian relaxation of the former.