Shortest Longest-Path Graph Orientations

Yuichi Asahiro, Jesper Jansson, Avraham A. Melkman, Eiji Miyano, Hirotaka Ono, Quan Xue, Shay Zakov

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

Abstract

We consider a graph orientation problem that can be viewed as a generalization of Minimum Graph Coloring. Our problem takes as input an undirected graph G= (V, E) in which every edge { u, v} ∈ E has two (potentially different and not necessarily positive) weights representing the lengths of its two possible directions (u, v) and (v, u), and asks for an orientation, i.e., an assignment of a direction to each edge of G, such that the length of a longest simple directed path in the resulting directed graph is minimized. A longest path in a graph is not always a maximal path when some edges have negative lengths, so the problem has two variants depending on whether all simple directed paths or maximal simple directed paths only are taken into account in the definition. We prove that the problems are NP-hard to approximate even if restricted to subcubic planar graphs, and develop fast polynomial-time algorithms for both problem variants for three classes of graphs: path graphs, cycle graphs, and star graphs.

Original languageEnglish
Title of host publicationComputing and Combinatorics - 29th International Conference, COCOON 2023, Proceedings
EditorsWeili Wu, Guangmo Tong
PublisherSpringer Science and Business Media Deutschland GmbH
Pages141-154
Number of pages14
ISBN (Print)9783031491894
DOIs
StatePublished - 1 Jan 2024
Event29th International Computing and Combinatorics Conference, COCOON 2023 - Hawaii, United States
Duration: 15 Dec 202317 Dec 2023

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume14422 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference29th International Computing and Combinatorics Conference, COCOON 2023
Country/TerritoryUnited States
CityHawaii
Period15/12/2317/12/23

Keywords

  • Algorithm
  • Computational complexity
  • Cycle graph
  • Graph coloring
  • Graph orientation
  • Path graph
  • Star graph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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