Route-enabling graph orientation problems

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

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

5 Citations (Scopus)

Abstract

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
Pages403-412
Number of pages10
DOIs
Publication statusPublished - Dec 1 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

Other

Other20th International Symposium on Algorithms and Computation, ISAAC 2009
CountryUnited States
CityHonolulu, HI
Period12/16/0912/18/09

Fingerprint

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

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Ito, T., Miyamoto, Y., Ono, H., Tamaki, H., & Uehara, R. (2009). Route-enabling graph orientation problems. In Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings (pp. 403-412). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5878 LNCS). https://doi.org/10.1007/978-3-642-10631-6_42

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

Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings. 2009. p. 403-412 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5878 LNCS).

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

Ito, T, Miyamoto, Y, Ono, H, Tamaki, H & Uehara, R 2009, Route-enabling graph orientation problems. in Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5878 LNCS, pp. 403-412, 20th International Symposium on Algorithms and Computation, ISAAC 2009, Honolulu, HI, United States, 12/16/09. https://doi.org/10.1007/978-3-642-10631-6_42
Ito T, Miyamoto Y, Ono H, Tamaki H, Uehara R. Route-enabling graph orientation problems. In Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings. 2009. p. 403-412. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-10631-6_42
Ito, Takehiro ; Miyamoto, Yuichiro ; Ono, Hirotaka ; Tamaki, Hisao ; Uehara, Ryuhei. / Route-enabling graph orientation problems. Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings. 2009. pp. 403-412 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{2b1a9903cba54fce95eadf0265565958,
title = "Route-enabling graph orientation problems",
abstract = "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.",
author = "Takehiro Ito and Yuichiro Miyamoto and Hirotaka Ono and Hisao Tamaki and Ryuhei Uehara",
year = "2009",
month = "12",
day = "1",
doi = "10.1007/978-3-642-10631-6_42",
language = "English",
isbn = "3642106307",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "403--412",
booktitle = "Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings",

}

TY - GEN

T1 - Route-enabling graph orientation problems

AU - Ito, Takehiro

AU - Miyamoto, Yuichiro

AU - Ono, Hirotaka

AU - Tamaki, Hisao

AU - Uehara, Ryuhei

PY - 2009/12/1

Y1 - 2009/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=75649091880&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=75649091880&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-10631-6_42

DO - 10.1007/978-3-642-10631-6_42

M3 - Conference contribution

AN - SCOPUS:75649091880

SN - 3642106307

SN - 9783642106309

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 403

EP - 412

BT - Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings

ER -