2026-09-20T02:17:19Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1195572026-06-06T00:49:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Erik D. Demaine.
Wu, Ray Hua
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2018-12-11T20:40:02Z
2018-12-11T20:40:02Z
2018
2018
http://hdl.handle.net/1721.1/119557
1076274217
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).
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.
by Ray Hua Wu.
M.Eng.
52 pages
eng
Massachusetts Institute of Technology
MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.
http://dspace.mit.edu/handle/1721.1/7582
Electrical Engineering and Computer Science.
Complexity of minesweeper with restricted number
Thesis
application/pdf
Publication
unknown
unknown
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="52f5dfe2-3cdf-4f85-acf2-705f4821a768">
<Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type>
<Language>eng</Language>
<Title>Complexity of minesweeper with restricted number</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2018</PublicationDate>
<Authors>
<Author>
<DisplayName>Wu, Ray Hua</DisplayName>
<Affiliation>
<OrgUnit>
</OrgUnit>
</Affiliation>
</Author>
</Authors>
<Editors>
</Editors>
<Publishers>
<Publisher>
<DisplayName>Massachusetts Institute of Technology</DisplayName>
<OrgUnit />
</Publisher>
</Publishers>
<License>http://dspace.mit.edu/handle/1721.1/7582</License>
<Keyword>Electrical Engineering and Computer Science.</Keyword>
<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.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>