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Parameterized Complexity of Non-Separating and Non-Disconnecting Paths and Sets

Authors Ankit Abhinav, Susobhan Bandopadhyay, Aritra Banik, Yasuaki Kobayashi , Shunsuke Nagano, Yota Otachi , Saket Saurabh

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Author Details

Ankit Abhinav
  • National Institute of Science, Education and Research, An OCC of Homi Bhabha National Institute, Bhubaneswar, Odisha, India
Susobhan Bandopadhyay
  • National Institute of Science, Education and Research, An OCC of Homi Bhabha National Institute, Bhubaneswar, Odisha, India
Aritra Banik
  • National Institute of Science, Education and Research, An OCC of Homi Bhabha National Institute, Bhubaneswar, Odisha, India
Yasuaki Kobayashi
  • Kyoto University, Kyoto, Japan
Shunsuke Nagano
  • Kyoto University, Kyoto, Japan
Yota Otachi
  • Nagoya University, Nagoya, Japan
Saket Saurabh
  • The Institute of Mathematical Sciences, HBNI, Chennai, India

Funding

  • Kobayashi, Yasuaki: JSPS KAKENHI Grant Numbers JP20H05793, JP20K19742, JP21H03499
  • Otachi, Yota: JSPS KAKENHI Grant Numbers JP18H04091, JP18K11168, JP18K11169, JP20H05793, JP21K11752.

Cite AsGet BibTex

Ankit Abhinav, Susobhan Bandopadhyay, Aritra Banik, Yasuaki Kobayashi, Shunsuke Nagano, Yota Otachi, and Saket Saurabh. Parameterized Complexity of Non-Separating and Non-Disconnecting Paths and Sets. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 6:1-6:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.MFCS.2022.6

Abstract

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
Keywords
  • Non-separating path
  • Parameterized complexity

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