Min-sum 2-paths problems

Trevor Fenner, Oded Lachish, Alexandru Popa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

An orientation of an undirected graph G is a directed graph obtained by replacing each edge {u,v} of G by exactly one of the arcs (u,v) or (v,u). In the min-sum k-paths orientation problem, the input is an undirected graph G and ordered pairs (s i ,t i ), where i ∈ {1,2,...,k}. The goal is to find an orientation of G that minimizes the sum over every i ∈ {1,2,...,k} of the distance from s i to t i . In the min-sum k edge-disjoint paths problem the input is the same, however the goal is to find for every i ∈ {1,2,...,k} a path between s i and t i so that these paths are edge-disjoint and the sum of their lengths is minimum. Note that, for every fixed k ≥ 2, the question of NP-hardness for the min-sum k-paths orientation problem and the min-sum k edge-disjoint paths problem have been open for more than two decades. We study the complexity of these problems when k = 2. We exhibit a PTAS for the min-sum 2-paths orientation problem. A by-product of this PTAS is a reduction from the min-sum 2-paths orientation problem to the min-sum 2 edge-disjoint paths problem. The implications of this reduction are: (i) an NP-hardness proof for the min-sum 2-paths orientation problem yields an NP-hardness proof for the min-sum 2 edge-disjoint paths problem, and (ii) any approximation algorithm for the min-sum 2 edge-disjoint paths problem can be used to construct an approximation algorithm for the min-sum 2-paths orientation problem with the same approximation guarantee and only an additive polynomial increase in the running time.

Original languageEnglish
Title of host publicationApproximation and Online Algorithms - 11th International Workshop, WAOA 2013, Revised Selected Papers
PublisherSpringer Verlag
Pages1-11
Number of pages11
ISBN (Print)9783319080000
DOIs
Publication statusPublished - Jan 1 2014
Event11th International Workshop on Approximation and Online Algorithms, WAOA 2013 - Sophia Antipolis, France
Duration: Sep 5 2013Sep 6 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8447 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other11th International Workshop on Approximation and Online Algorithms, WAOA 2013
CountryFrance
CitySophia Antipolis
Period9/5/139/6/13

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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