Minesweeper on graphs

Minesweeper is a popular single player game. It has been shown that the Minesweeper consistency problem is NP-complete and the Minesweeper counting problem is #P-complete. In this paper, we present efficient algorithms for solving these problems for Minesweeper graphs with bounded treewidth. Our algorithms turn out to be much better than those based directly on dynamic programming. The algorithms mostly use of algebraic operations on multivariate polynomials, so that one may use existing software to implement them easily.