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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.

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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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