Route-enabling graph orientation problems

Takehiro Ito, Yuichiro Miyamoto, Hirotaka Ono, Hisao Tamaki, Ryuhei Uehara

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

6 Citations (Scopus)


Given an undirected and edge-weighted graph G together with a set of ordered vertex-pairs, called st-pairs, we consider the problems of finding an orientation of all edges in G: min-sum orientation is to minimize the sum of the shortest directed distances between all st-pairs; and min-max orientation is to minimize the maximum shortest directed distance among all st-pairs. In this paper, we first show that both problems are strongly NP-hard for planar graphs even if all edge-weights are identical, and that both problems can be solved in polynomial time for cycles. We then consider the problems restricted to cacti, which form a graph class that contains trees and cycles but is a subclass of planar graphs. Then, min-sum orientation is solvable in polynomial time, whereas min-max orientation remains NP-hard even for two st-pairs. However, based on LP-relaxation, we present a polynomial-time 2-approximation algorithm for min-max orientation. Finally, we give a fully polynomial-time approximation scheme (FPTAS) for min-max orientation on cacti if the number of st-pairs is a fixed constant.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings
Number of pages10
Publication statusPublished - 2009
Event20th International Symposium on Algorithms and Computation, ISAAC 2009 - Honolulu, HI, United States
Duration: Dec 16 2009Dec 18 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5878 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other20th International Symposium on Algorithms and Computation, ISAAC 2009
Country/TerritoryUnited States
CityHonolulu, HI

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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