TY - GEN

T1 - Shortest Longest-Path Graph Orientations

AU - Asahiro, Yuichi

AU - Jansson, Jesper

AU - Melkman, Avraham A.

AU - Miyano, Eiji

AU - Ono, Hirotaka

AU - Xue, Quan

AU - Zakov, Shay

N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

PY - 2024/1/1

Y1 - 2024/1/1

N2 - 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.

AB - 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.

KW - Algorithm

KW - Computational complexity

KW - Cycle graph

KW - Graph coloring

KW - Graph orientation

KW - Path graph

KW - Star graph

UR - http://www.scopus.com/inward/record.url?scp=85180531191&partnerID=8YFLogxK

U2 - 10.1007/978-3-031-49190-0_10

DO - 10.1007/978-3-031-49190-0_10

M3 - Conference contribution

AN - SCOPUS:85180531191

SN - 9783031491894

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

SP - 141

EP - 154

BT - Computing and Combinatorics - 29th International Conference, COCOON 2023, Proceedings

A2 - Wu, Weili

A2 - Tong, Guangmo

PB - Springer Science and Business Media Deutschland GmbH

T2 - 29th International Computing and Combinatorics Conference, COCOON 2023

Y2 - 15 December 2023 through 17 December 2023

ER -