TY - GEN
T1 - Kernels for the Disjoint Paths Problem on Subclasses of Chordal Graphs
AU - Chaudhary, Juhi
AU - Gahlawat, Harmender
AU - Włodarczyk, Michal
AU - Zehavi, Meirav
N1 - Publisher Copyright:
© 2023 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.
PY - 2023/12/1
Y1 - 2023/12/1
N2 - Given an undirected graph G and a multiset of k terminal pairs X, the Vertex-Disjoint Paths (VDP) and Edge-Disjoint Paths (EDP) problems ask whether G has k pairwise internally vertexdisjoint paths and k pairwise edge-disjoint paths, respectively, connecting every terminal pair in X. In this paper, we study the kernelization complexity of VDP and EDP on subclasses of chordal graphs. For VDP, we design a 4k vertex kernel on split graphs and an O(k2) vertex kernel on well-partitioned chordal graphs. We also show that the problem becomes polynomial-time solvable on threshold graphs. For EDP, we first prove that the problem is NP-complete on complete graphs. Then, we design an O(k2.75) vertex kernel for EDP on split graphs, and improve it to a 7k+1 vertex kernel on threshold graphs. Lastly, we provide an O(k2) vertex kernel for EDP on block graphs and a 2k + 1 vertex kernel for clique paths. Our contributions improve upon several results in the literature, as well as resolve an open question by Heggernes et al.
AB - Given an undirected graph G and a multiset of k terminal pairs X, the Vertex-Disjoint Paths (VDP) and Edge-Disjoint Paths (EDP) problems ask whether G has k pairwise internally vertexdisjoint paths and k pairwise edge-disjoint paths, respectively, connecting every terminal pair in X. In this paper, we study the kernelization complexity of VDP and EDP on subclasses of chordal graphs. For VDP, we design a 4k vertex kernel on split graphs and an O(k2) vertex kernel on well-partitioned chordal graphs. We also show that the problem becomes polynomial-time solvable on threshold graphs. For EDP, we first prove that the problem is NP-complete on complete graphs. Then, we design an O(k2.75) vertex kernel for EDP on split graphs, and improve it to a 7k+1 vertex kernel on threshold graphs. Lastly, we provide an O(k2) vertex kernel for EDP on block graphs and a 2k + 1 vertex kernel for clique paths. Our contributions improve upon several results in the literature, as well as resolve an open question by Heggernes et al.
KW - Edge-Disjoint Paths Problem
KW - Kernelization
KW - Parameterized Complexity
KW - Vertex-Disjoint Paths Problem
UR - http://www.scopus.com/inward/record.url?scp=85180553752&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.IPEC.2023.10
DO - 10.4230/LIPIcs.IPEC.2023.10
M3 - Conference contribution
AN - SCOPUS:85180553752
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 18th International Symposium on Parameterized and Exact Computation, IPEC 2023
A2 - Misra, Neeldhara
A2 - Wahlstrom, Magnus
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 18th International Symposium on Parameterized and Exact Computation, IPEC 2023
Y2 - 6 September 2023 through 8 September 2023
ER -