International Journal of Game Theory

, Volume 47, Issue 2, pp 487–508

# Ice sliding games

• Paul Dorbec
• Éric Duchêne
• André Fabbri
• Julien Moncel
• Aline Parreau
• Éric Sopena
Original Paper

## 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

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© Springer-Verlag GmbH Germany, part of Springer Nature 2017

## Authors and Affiliations

• Paul Dorbec
• 1
• Éric Duchêne
• 2
• André Fabbri
• 2
• Julien Moncel
• 3
• Aline Parreau
• 2
• Éric Sopena
• 1
1. 1.Univ. Bordeaux, Bordeaux INP, CNRS, LaBRI, UMR5800TalenceFrance
2. 2.Université de Lyon, CNRS, Université Lyon 1, LIRIS, UMR 5205LyonFrance
3. 3.CNRS, LAAS, Université de ToulouseToulouseFrance