Finding the minimum-weight k-path

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

Abstract

Given a weighted n-vertex graph G with integer edge-weights taken from a range [-M,M], we show that the minimum-weight simple path visiting k vertices can be found in time Õ(2kpoly(k)Mnω) = O*(2kM). If the weights are reals in [1,M], we provide a (1 + ε)-approximation which has a running time of Õ(2kpoly(k) nω (log log M + 1/ε)). For the more general problem of k-tree, in which we wish to find a minimum-weight copy of a k-node tree T in a given weighted graph G, under the same restrictions on edge weights respectively, we give an exact solution of running time Õ(2 kpoly(k)Mn3) and a (1 + ε)-approximate solution of running time Õ(2kpoly(k)n3(log log M + 1/ε)). All of the above algorithms are randomized with a polynomially-small error probability.

Original languageEnglish
Title of host publicationAlgorithms and Data Structures - 13th International Symposium, WADS 2013, Proceedings
Pages390-401
Number of pages12
DOIs
StatePublished - 2013
Event13th International Symposium on Algorithms and Data Structures, WADS 2013 - London, ON, Canada
Duration: 12 Aug 201314 Aug 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8037 LNCS

Conference

Conference13th International Symposium on Algorithms and Data Structures, WADS 2013
Country/TerritoryCanada
CityLondon, ON
Period12/08/1314/08/13

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

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