TY - GEN
T1 - Min-Sum Disjoint Paths on Subclasses of Chordal Graphs
AU - Menashe, Bar
AU - Zehavi, Meirav
N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.
PY - 2025/1/1
Y1 - 2025/1/1
N2 - We study the optimization version of the classic Disjoint Paths problem, known as Min-Sum Disjoint Paths, as well as its restriction to shortest paths, known as Disjoint Shortest Paths. Both problems are notoriously hard in the sense that very few positive results are known in their context even when confined to grids, in contrast to the classic Disjoint Paths problem, despite significant research efforts in recent years. In light of this, we focus on restricted graph classes, being subclasses of chordal graphs: specifically, we consider the classes of split graphs, well-partitioned chordal graphs, and threshold graphs. For each of the two problems and each of these graph classes, we provide either a polynomial-time algorithm or a fixed-parameter algorithm (when a polynomial-time algorithm is unlikely to exist).
AB - We study the optimization version of the classic Disjoint Paths problem, known as Min-Sum Disjoint Paths, as well as its restriction to shortest paths, known as Disjoint Shortest Paths. Both problems are notoriously hard in the sense that very few positive results are known in their context even when confined to grids, in contrast to the classic Disjoint Paths problem, despite significant research efforts in recent years. In light of this, we focus on restricted graph classes, being subclasses of chordal graphs: specifically, we consider the classes of split graphs, well-partitioned chordal graphs, and threshold graphs. For each of the two problems and each of these graph classes, we provide either a polynomial-time algorithm or a fixed-parameter algorithm (when a polynomial-time algorithm is unlikely to exist).
KW - Chordal Graphs
KW - Parameterized Complexity
KW - Vertex-Disjoint Paths Problem
UR - https://www.scopus.com/pages/publications/86000258655
U2 - 10.1007/978-981-96-2845-2_18
DO - 10.1007/978-981-96-2845-2_18
M3 - Conference contribution
SN - 9789819628445
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 281
EP - 295
BT - WALCOM
A2 - Nakano, Shin-ichi
A2 - Xiao, Mingyu
PB - Springer Science and Business Media Deutschland GmbH
T2 - 19th International Conference and Workshops on Algorithms and Computation, WALCOM 2025
Y2 - 28 February 2025 through 2 March 2025
ER -