A note on the prize collecting traveling salesman problem
Mathematical Programming: Series A and B
The Complexity of Multiterminal Cuts
SIAM Journal on Computing
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
An improved approximation algorithm for MULTIWAY CUT
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications
SIAM Journal on Computing
Rounding Algorithms for a Geometric Embedding of Minimum Multiway Cut
Mathematics of Operations Research
Approximating the k-multicut problem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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
Optimal hierarchical decompositions for congestion minimization in networks
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
On the complexity of the multicut problem in bounded tree-width graphs and digraphs
Discrete Applied Mathematics
Approximating Generalized Multicut on Trees
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
A Bicriteria Approximation Algorithm for Generalized k-Multicut in Trees
CSO '09 Proceedings of the 2009 International Joint Conference on Computational Sciences and Optimization - Volume 02
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Detecting high log-densities: an O(n¼) approximation for densest k-subgraph
Proceedings of the forty-second ACM symposium on Theory of computing
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Approximation algorithms for requirement cut on graphs
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
On the generalized multiway cut in trees problem
Journal of Combinatorial Optimization
A new approximation algorithm for the Selective Single-Sink Buy-at-Bulk problem in network design
Journal of Combinatorial Optimization
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Given a graph G=(V,E) with nonnegative costs defined on edges, a positive integer k, and a collection of q terminal sets D={S"1,S"2,...,S"q}, where each S"i is a subset of V(G), the Generalized k-Multicut problem asks to find a set of edges C@?E(G) at the minimum cost such that its removal from G cuts at least k terminal sets in D. A terminal subset S"i is cut by C if all terminals in S"i are disconnected from one another by removing C from G. This problem is a generalization of the k-Multicut problem and the Multiway Cut problem. The famous Densest k-Subgraph problem can be reduced to the Generalized k-Multicut problem in trees via an approximation preserving reduction. In this paper, we first give an O(q)-approximation algorithm for the Generalized k-Multicut problem when the input graph is a tree. The algorithm is based on a mixed strategy of LP-rounding and greedy approach. Moreover, the algorithm is applicable to deal with a class of NP-hard partial optimization problems. As its extensions, we then show that the algorithm can be used to give O(qlogn)-approximation for the Generalized k-Multicut problem in undirected graphs and O(q)-approximation for the k-Forest problem.