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Reconfiguring Simple s, t Hamiltonian Paths in Rectangular Grid Graphs

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Combinatorial Algorithms (IWOCA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12757))

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Abstract

We study the following reconfiguration problem: given two s, t Hamiltonian paths connecting diagonally opposite corners s and t of a rectangular grid graph G, can we transform one to the other using only local operations in the grid cells? In this work, we introduce the notion of simple s, t Hamiltonian paths, and give an algorithm to reconfigure such paths of G in O(|G|) time using local operations in unit grid cells. We achieve our algorithmic result by proving a combinatorial structure theorem for simple s, t Hamiltonian paths in rectangular grid graphs.

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Authors and Affiliations

  1. Department of Computer Science, University of Victoria, Victoria, BC, Canada

    Rahnuma Islam Nishat, Venkatesh Srinivasan & Sue Whitesides

Authors
  1. Rahnuma Islam Nishat
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  2. Venkatesh Srinivasan
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  3. Sue Whitesides
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Corresponding author

Correspondence to Rahnuma Islam Nishat .

Editor information

Editors and Affiliations

  1. University of Ottawa, Ottawa, ON, Canada

    Paola Flocchini

  2. University of Ottawa, Ottawa, ON, Canada

    Lucia Moura

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Nishat, R.I., Srinivasan, V., Whitesides, S. (2021). Reconfiguring Simple s, t Hamiltonian Paths in Rectangular Grid Graphs. In: Flocchini, P., Moura, L. (eds) Combinatorial Algorithms. IWOCA 2021. Lecture Notes in Computer Science(), vol 12757. Springer, Cham. https://doi.org/10.1007/978-3-030-79987-8_35

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  • DOI: https://doi.org/10.1007/978-3-030-79987-8_35

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  • Print ISBN: 978-3-030-79986-1

  • Online ISBN: 978-3-030-79987-8

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