Lowest degree κ-Spanner: Approximation and hardness

Eden Chlamtáč, Michael Dinitz

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

8 Scopus citations

Abstract

A κ-spanner is a subgraph in which distances are approximately preserved, up to some given stretch factor κ. We focus on the following problem: Given a graph and a value κ, can we find a κ-spanner that minimizes the maximum degree? While reasonably strong bounds are known for some spanner problems, they almost all involve minimizing the total number of edges. Switching the objective to the degree introduces significant new challenges, and currently the only known approximation bound is an Õ (δ3-2√2)-approximation for the special case when κ = 2 [Chlamtáč, Dinitz, Krauthgamer FOCS 2012] (where δ is the maximum degree in the input graph). In this paper we give the first non-trivial algorithm and polynomial-factor hardness of approximation for the case of general k. Specifically, we give an LP-based Õ(δ(1-1/k)2 )-approximation and prove that it is hard to approximate the optimum to within δ ω (1/k) when the graph is undirected, and to within δ ω(1) when it is directed.

Original languageEnglish
Title of host publicationLeibniz International Proceedings in Informatics, LIPIcs
EditorsJose D. P. Rolim, Cristopher Moore, Nikhil R. Devanur, Klaus Jansen
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages80-95
Number of pages16
ISBN (Electronic)9783939897743
DOIs
StatePublished - 1 Sep 2014
Event17th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2014 and the 18th International Workshop on Randomization and Computation, RANDOM 2014 - Barcelona, Spain
Duration: 4 Sep 20146 Sep 2014

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume28
ISSN (Print)1868-8969

Conference

Conference17th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2014 and the 18th International Workshop on Randomization and Computation, RANDOM 2014
Country/TerritorySpain
CityBarcelona
Period4/09/146/09/14

Keywords

  • Approximation algorithms
  • Graph spanners
  • Hardness of approximation

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