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Parameterized Shortest Path Reconfiguration

Authors Nicolas Bousquet , Kshitij Gajjar, Abhiruk Lahiri , Amer E. Mouawad

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Author Details

Nicolas Bousquet
  • Univ. Lyon, LIRIS, CNRS, Université Claude Bernard Lyon 1, Villeurbanne, France
Kshitij Gajjar
  • Centre for Security, Theory & Algorithmic Research (CSTAR), International Institute of Information Technology, Hyderabad (IIIT-H), India
Abhiruk Lahiri
  • Department of Computer Science, Heinrich Heine University, Düsseldorf, Germany
Amer E. Mouawad
  • Department of Computer Science, American University of Beirut, Lebanon

Funding

  • Lahiri, Abhiruk: Partly supported by SFF grant "Theoretical AI" of HHU Düsseldorf and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - project number 456558332.

Cite As Get BibTex

Nicolas Bousquet, Kshitij Gajjar, Abhiruk Lahiri, and Amer E. Mouawad. Parameterized Shortest Path Reconfiguration. In 19th International Symposium on Parameterized and Exact Computation (IPEC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 321, pp. 23:1-23:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.IPEC.2024.23

Abstract

An st-shortest path, or st-path for short, in a graph G is a shortest (induced) path from s to t in G. Two st-paths are said to be adjacent if they differ on exactly one vertex. A reconfiguration sequence between two st-paths P and Q is a sequence of adjacent st-paths starting from P and ending at Q. Deciding whether there exists a reconfiguration sequence between two given st-paths is known to be PSPACE-complete, even on restricted classes of graphs such as graphs of bounded bandwidth (hence pathwidth). On the positive side, and rather surprisingly, the problem is polynomial-time solvable on planar graphs. In this paper, we study the parameterized complexity of the Shortest Path Reconfiguration (SPR) problem. We show that SPR is W[1]-hard parameterized by k + 𝓁, even when restricted to graphs of bounded (constant) degeneracy; here k denotes the number of edges on an st-path, and 𝓁 denotes the length of a reconfiguration sequence from P to Q. We complement our hardness result by establishing the fixed-parameter tractability of SPR parameterized by 𝓁 and restricted to nowhere-dense classes of graphs. Additionally, we establish fixed-parameter tractability of SPR when parameterized by the treedepth, by the cluster-deletion number, or by the modular-width of the input graph.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • combinatorial reconfiguration
  • shortest path reconfiguration
  • parameterized complexity
  • structural parameters
  • treedepth
  • cluster deletion number
  • modular width

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