Ice sliding games

Paul Dorbec (), Éric Duchêne (), André Fabbri (), Julien Moncel (), Aline Parreau () and Éric Sopena ()
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Paul Dorbec: Univ. Bordeaux, Bordeaux INP, CNRS, LaBRI, UMR5800
Éric Duchêne: Université de Lyon, CNRS, Université Lyon 1, LIRIS, UMR 5205
André Fabbri: Université de Lyon, CNRS, Université Lyon 1, LIRIS, UMR 5205
Julien Moncel: CNRS, LAAS, Université de Toulouse
Aline Parreau: Université de Lyon, CNRS, Université Lyon 1, LIRIS, UMR 5205
Éric Sopena: Univ. Bordeaux, Bordeaux INP, CNRS, LaBRI, UMR5800

International Journal of Game Theory, 2018, vol. 47, issue 2, No 6, 487-508

Abstract: Abstract This paper deals with sliding games, which are a variant of the better known pushpush game. On a given structure (grid, torus...), a robot can move in a specific set of directions, and stops when it hits a block or boundary of the structure. The objective is to place the minimum number of blocks such that the robot can visit all the possible positions of the structure. In particular, we give the exact value of this number when playing on a rectangular grid and a torus. Other variants of this game are also considered, by constraining the robot to stop on each case, or by replacing blocks by walls.

Keywords: Combinatorial game theory; Graph theory; Sliding games (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s00182-017-0607-5

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