Minesweeper on graphs

Shahar Golan

doi:10.1016/j.amc.2011.01.046

Minesweeper on graphs

Shahar Golan

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	6616-6623
Number of pages	8
Journal	Applied Mathematics and Computation
Volume	217
Issue number	14
DOIs	https://doi.org/10.1016/j.amc.2011.01.046
State	Published - 15 Mar 2011

Keywords

CSP
Consistency
Constraint satisfaction
Counting problem
Dynamic programming
Generating polynomials
Minesweeper
Treewidth

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2011.01.046

Cite this

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title = "Minesweeper on graphs",

abstract = "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.",

keywords = "CSP, Consistency, Constraint satisfaction, Counting problem, Dynamic programming, Generating polynomials, Minesweeper, Treewidth",

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AB - 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.

KW - CSP

KW - Consistency

KW - Constraint satisfaction

KW - Counting problem

KW - Dynamic programming

KW - Generating polynomials

KW - Minesweeper

KW - Treewidth

UR - https://www.scopus.com/pages/publications/79952002320

U2 - 10.1016/j.amc.2011.01.046

DO - 10.1016/j.amc.2011.01.046

M3 - Article

AN - SCOPUS:79952002320

SN - 0096-3003

VL - 217

SP - 6616

EP - 6623

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 14

ER -

Minesweeper on graphs

Abstract

Keywords

ASJC Scopus subject areas

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