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 -