TY - GEN

T1 - Partial multicuts in trees

AU - Levin, Asaf

AU - Segev, Danny

PY - 2006

Y1 - 2006

N2 - Let T = (V, E) be an undirected tree, in which each edge is associated with a non-negative cost, and let {s1, t1}, . . . ,{s k,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 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.

AB - Let T = (V, E) be an undirected tree, in which each edge is associated with a non-negative cost, and let {s1, t1}, . . . ,{s k,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 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.

UR - http://www.scopus.com/inward/record.url?scp=33745623432&partnerID=8YFLogxK

U2 - 10.1007/11671411_25

DO - 10.1007/11671411_25

M3 - Conference contribution

AN - SCOPUS:33745623432

SN - 3540322078

SN - 9783540322078

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 320

EP - 333

BT - Approximation and Online Algorithms - Third International Workshop, WAOA 2005, Revised Selected Papers

T2 - 3rd International Workshop on Approximation and Online Algorithms, WAOA 2005

Y2 - 6 October 2005 through 7 October 2005

ER -