Complexity of minesweeper with restricted number
Name
1076274217-MIT.pdf
Description
Full printable version
Size
357.45 KB
Format
Adobe PDF
Checksum (MD5)
4df39527b31482e41d56ba6f601ffa94
Author(s)
Wu, Ray Hua
Advisor(s)
Erik D. Demaine.
Date Issued
2018
Publisher
Massachusetts Institute of Technology
Abstract
We consider the Minesweeper consistency problem (is a given partially completed board consistent with some mine placement?) when the set of numbers that may appear on a Minesweeper board is restricted. First, we analyze the possible sets of numbers that could exist in legal rectangular Minesweeper boards, proving either possibility or impossibility for 509 of the 512 subsets of {0, 1, 2, 3, 4, 5, 6, 7, 8} (leaving 3 subsets as open problems), and thus make conclusions on the relations among some restricted-set Minesweeper consistency problems. We prove either inclusion in P or NP-completeness for the restricted-set Minesweeper consistency problem for 134 of the 512 subsets of the set of numbers above. In particular, we show that {0,1}-Minesweeper consistency is NP-complete, while {0}-Minesweeper consistency and {1}-Minesweeper consistency are in P. We also suggest a few more dimensions in which the Minesweeper consistency problem could be analyzed.
Description
Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2018.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 51-52).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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