The Complexity of Multiterminal Cuts
SIAM Journal on Computing
Improved performance of the greedy algorithm for partial cover
Information Processing Letters
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Using homogeneous weights for approximating the partial cover problem
Journal of Algorithms
Approximation algorithms
A new greedy approach for facility location problems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications
SIAM Journal on Computing
Approximation algorithms for partial covering problems
Journal of Algorithms
On the Hardness of Approximating Multicut and Sparsest-Cut
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Approximating the k-multicut problem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A unified approach to approximating partial covering problems
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Path hitting in acyclic graphs
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
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
Approximating Generalized Multicut on Trees
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
An approximation algorithm to the k-Steiner Forest problem
Theoretical Computer Science
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
Approximation algorithms for k-hurdle problems
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
An approximation algorithm for the Generalized k-Multicut problem
Discrete Applied Mathematics
| Hi-index | 0.00 |
Let T = (V,E) be an undirected tree, in which each edge is associated with a non-negative cost, and let { s1, t1 }, ..., { sk, tk } be a collection of k distinct pairs of vertices. Given a requirement parameter t ≤ k, the partial multicut on a tree problem asks to find a minimum cost set of edges whose removal from T disconnects at least t out of these k pairs. This problem generalizes the well-known multicut on a tree problem, in which we are required to disconnect all given pairs. The main contribution of this paper is an (${\frac{8}{3}}+{\epsilon}$)-approximation algorithm for partial multicut on a tree, whose run time is strongly polynomial for any fixed ε 0. This result is achieved by introducing problem-specific insight to the general framework of using the Lagrangian relaxation technique in approximation algorithms. Our algorithm utilizes a heuristic for the closely related prize-collecting variant, in which we are not required to disconnect all pairs, but rather incur penalties for failing to do so. We provide a Lagrangian multiplier preserving algorithm for the latter problem, with an approximation factor of 2. Finally, we present a new 2-approximation algorithm for multicut on a tree, based on LP-rounding.