Partial Multicuts in Trees

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 + )-approximation algorithm for partial multicut on a tree, whose run time is strongly polynomial for any fixed > 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 failin...

• Type: Conference
• Year: 2005
• Where: WAOA
• Authors: Asaf Levin, Danny Segev
• Keywords: Algorithm, Partial Multicut, Tree Problem, WAOA 2005