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.
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Butko N, Lehmann KA, Ramenzoni V (2006) Ricochet robots—a case study for human complex problem solving. Project thesis from the Complex System Summer School, Santa Fe Institute
Demaine E (2001) Playing games with algorithms: algorithmic combinatorial game theory. In: Proceedings of the 26th international symposium on mathematical foundations of computer science
Engels B, Kamphans T (2005) On the complexity of Randolph’s Robot Game, Technical Report
Gonçalves D, Pinlou A, Rao M, Thomassé S (2011) The domination number of grids. SIAM J Discrete Math 25(3):1443–1453
Hartline JR, Libeskind-Hadas R (2003) The computational complexity of motion planning. SIAM Rev 45(3):543–557
Hock M (2001) Exploring the complexity of the UFO puzzle. Undergraduate thesis, Carnegie Mellon University. http://www.cs.cmu.edu/afs/cs/user/mjs/ftp/thesis-02/hock.ps
Klobucar A (2004) Total domination numbers of cartesian products. Math Commun 9:35–44
TCS questions & answers Website (2012). http://cstheory.stackexchange.com/questions/10813/what-is-the-known-complexity-of-this-game-similar-to-pushpush-1
This research is supported by the ANR-14-CE25-0006 project of the French National Research Agency.
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Dorbec, P., Duchêne, É., Fabbri, A. et al. Ice sliding games. Int J Game Theory 47, 487–508 (2018). https://doi.org/10.1007/s00182-017-0607-5
- Combinatorial game theory
- Graph theory
- Sliding games