Partial multicuts in trees

Asaf Levin, Danny Segev

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish
Title of host publicationApproximation and Online Algorithms - Third International Workshop, WAOA 2005, Revised Selected Papers
Number of pages14
StatePublished - 2006
Externally publishedYes
Event3rd International Workshop on Approximation and Online Algorithms, WAOA 2005 - Palma de Mallorca, Spain
Duration: 6 Oct 20057 Oct 2005

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3879 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference3rd International Workshop on Approximation and Online Algorithms, WAOA 2005
CityPalma de Mallorca

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


Dive into the research topics of 'Partial multicuts in trees'. Together they form a unique fingerprint.

Cite this