‘Minesweeper’ and spectrum of discrete Laplacians

@article{German2010MinesweeperAS,
  title={‘Minesweeper’ and spectrum of discrete Laplacians},
  author={Oleg German and Evgeny Lakshtanov},
  journal={Applicable Analysis},
  year={2010},
  volume={89},
  pages={1907 - 1916}
}
The article is devoted to a problem inspired by the ‘Minesweeper’ computer game. It is shown that certain configurations of open cells guarantee the existence and the uniqueness of solution. Mathematically the problem is reduced to some spectral properties of discrete differential operators. It is shown how the uniqueness can be used to create a new game which preserves the spirit of ‘Minesweeper’ but does not require a computer. 

Minesweeper on graphs

  • Shahar Golan
  • Computer Science, Mathematics
    Appl. Math. Comput.
  • 2011

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References

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The Minesweeper Game: Percolation and Complexity

A model motivated by the minesweeper game, in which one starts with the percolation of mines on the lattice ℤd, and then tries to find an infinite path of mine-free sites, is studied.

How cellular automaton plays Minesweeper

Minesweeper is NP-complete

NP-completeness Many programming p rob lems require the design of an algori thm which has a "yes" or "no" ou tput for each input, and there are two classes of p rob l ems that are of grea tes t in teres t for complexi tytheoris ts.