Route-enabling graph orientation problems

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

Research output: Contribution to journalArticle

Abstract

Given an undirected and edge-weighted graph G together with a set of ordered vertex-pairs, called st-pairs, we consider two 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. Note that these shortest directed paths for st-pairs are not necessarily edge-disjoint. 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 polynomialtime 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
Pages (from-to)317-338
Number of pages22
JournalAlgorithmica
Volume65
Issue number2
DOIs
Publication statusPublished - Feb 1 2013

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Polynomials
Graph in graph theory
Cactus
Approximation algorithms
Planar graph
Polynomial time
NP-complete problem
Minimise
Fully Polynomial Time Approximation Scheme
Cycle
LP Relaxation
Graph Classes
Weighted Graph
Approximation Algorithms
Disjoint
Path
Vertex of a graph

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics

Cite this

Ito, T., Miyamoto, Y., Ono, H., Tamaki, H., & Uehara, R. (2013). Route-enabling graph orientation problems. Algorithmica, 65(2), 317-338. https://doi.org/10.1007/s00453-011-9589-z

Route-enabling graph orientation problems. / Ito, Takehiro; Miyamoto, Yuichiro; Ono, Hirotaka; Tamaki, Hisao; Uehara, Ryuhei.

In: Algorithmica, Vol. 65, No. 2, 01.02.2013, p. 317-338.

Research output: Contribution to journalArticle

Ito, T, Miyamoto, Y, Ono, H, Tamaki, H & Uehara, R 2013, 'Route-enabling graph orientation problems', Algorithmica, vol. 65, no. 2, pp. 317-338. https://doi.org/10.1007/s00453-011-9589-z
Ito T, Miyamoto Y, Ono H, Tamaki H, Uehara R. Route-enabling graph orientation problems. Algorithmica. 2013 Feb 1;65(2):317-338. https://doi.org/10.1007/s00453-011-9589-z
Ito, Takehiro ; Miyamoto, Yuichiro ; Ono, Hirotaka ; Tamaki, Hisao ; Uehara, Ryuhei. / Route-enabling graph orientation problems. In: Algorithmica. 2013 ; Vol. 65, No. 2. pp. 317-338.
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