eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-08-22
6:1
6:15
10.4230/LIPIcs.MFCS.2022.6
article
Parameterized Complexity of Non-Separating and Non-Disconnecting Paths and Sets
Abhinav, Ankit
1
Bandopadhyay, Susobhan
1
Banik, Aritra
1
Kobayashi, Yasuaki
2
https://orcid.org/0000-0003-3244-6915
Nagano, Shunsuke
2
Otachi, Yota
3
https://orcid.org/0000-0002-0087-853X
Saurabh, Saket
4
National Institute of Science, Education and Research, An OCC of Homi Bhabha National Institute, Bhubaneswar, Odisha, India
Kyoto University, Kyoto, Japan
Nagoya University, Nagoya, Japan
The Institute of Mathematical Sciences, HBNI, Chennai, India
For a connected graph G = (V, E) and s, t ∈ V, a non-separating s-t path is a path P between s and t such that the set of vertices of P does not separate G, that is, G - V(P) is connected. An s-t path P is non-disconnecting if G - E(P) is connected. The problems of finding shortest non-separating and non-disconnecting paths are both known to be NP-hard. In this paper, we consider the problems from the viewpoint of parameterized complexity. We show that the problem of finding a non-separating s-t path of length at most k is W[1]-hard parameterized by k, while the non-disconnecting counterpart is fixed-parameter tractable (FPT) parameterized by k. We also consider the shortest non-separating path problem on several classes of graphs and show that this problem is NP-hard even on bipartite graphs, split graphs, and planar graphs. As for positive results, the shortest non-separating path problem is FPT parameterized by k on planar graphs and on unit disk graphs (where no s, t is given). Further, we give a polynomial-time algorithm on chordal graphs if k is the distance of the shortest path between s and t.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol241-mfcs2022/LIPIcs.MFCS.2022.6/LIPIcs.MFCS.2022.6.pdf
Non-separating path
Parameterized complexity