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
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
The t-Vertex Cover Problem: Extending the Half Integrality Framework with Budget Constraints
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
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
Strongly polynomial-time approximation for a class of bicriteria problems
Operations Research Letters
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Theoretical Computer Science
| Hi-index | 5.23 |
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 (8/3 + ε)-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.