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Grid Graphs with Diagonal Edges and the Complexity of Xmas Mazes

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Fun with Algorithms (FUN 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7288))

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Abstract

We investigate the computational complexity of some maze problems, namely the reachability problem for (undirected) grid graphs with diagonal edges, and the solvability of Xmas tree mazes. Simply speaking, in the latter game one has to move sticks of a certain length through a maze, ending in a particular game situation. It turns out that when the number of sticks is bounded by some constant, these problems are closely related to the grid graph problems with diagonals. If on the other hand an unbounded number of sticks is allowed, then the problem of solving such a maze becomes PSPACE-complete. Hardness is shown via a reduction from the nondeterministic constraint logic (NCL) of [E. D. Demaine, R. A. Hearn: A uniform framework or modeling computations as games. Proc. CCC, 2008] to Xmas tree mazes.

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References

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Authors and Affiliations

  1. Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392, Giessen, Germany

    Markus Holzer & Sebastian Jakobi

Authors
  1. Markus Holzer
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  2. Sebastian Jakobi
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Editors and Affiliations

  1. School of Computer Science, Carleton University, 1125 Col. By Dr., K1S 5B6, Ottawa, ON, Canada

    Evangelos Kranakis

  2. Department of Mathematics and Computer Science, Wesleyan University, 06459, Middleton, CT, USA

    Danny Krizanc

  3. Dipartimento di Scienze Ambientali, Informatica e Statistica, Università Ca’ Foscari, Via Torino 155, 30172, Mestre (Ve), Italy

    Flaminia Luccio

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© 2012 Springer-Verlag Berlin Heidelberg

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Holzer, M., Jakobi, S. (2012). Grid Graphs with Diagonal Edges and the Complexity of Xmas Mazes. In: Kranakis, E., Krizanc, D., Luccio, F. (eds) Fun with Algorithms. FUN 2012. Lecture Notes in Computer Science, vol 7288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30347-0_23

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  • DOI: https://doi.org/10.1007/978-3-642-30347-0_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30346-3

  • Online ISBN: 978-3-642-30347-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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