Approximate k-Steiner forests via the Lagrangian relaxation technique with internal preprocessing

Danny Segev, Gil Segev

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

Abstract

An instance of the k-Steiner forest problem consists of an undirected graph G = ( V, E), the edges of which are associated with non-negative costs, and a collection D = {(si, ti): 1 ≤ i ≤ d} of distinct pairs of vertices, interchangeably referred to as demands. We say that a forest Fscr; ⊆ G connects a demand (si, ti) when it contains an si-ti path. Given a requirement parameter k ≤ |D|, the goal is to find a minimum cost forest that connects at least k demands in D. This problem has recently been studied by Hajiaghayi and Jain [SODA '06], whose main contribution in this context was to relate the inapproximability of k-Steiner forest to that of the dense k-subgraph problem. However, Hajiaghayi and Jain did not provide any algorithmic result for the respective settings, and posed this objective as an important direction for future research. In this paper, we present the first non-trivial approximation algorithm for the A-Steiner forest problem, which is based on a novel extension of the Lagrangian relaxation technique. Specifically, our algorithm constructs a feasible forest whose cost is within a factor of O(min{n2/3, √d} · log d) of optimal, where n is the number of vertices in the input graph and d is the number of demands.

Original languageEnglish
Title of host publicationAlgorithms, ESA 2006 - 14th Annual European Symposium, Proceedings
PublisherSpringer Verlag
Pages600-611
Number of pages12
ISBN (Print)3540388753, 9783540388753
DOIs
StatePublished - 2006
Externally publishedYes
Event14th Annual European Symposium on Algorithms, ESA 2006 - Zurich, Switzerland
Duration: 11 Sep 200613 Sep 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4168 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference14th Annual European Symposium on Algorithms, ESA 2006
Country/TerritorySwitzerland
CityZurich
Period11/09/0613/09/06

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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