Complexity of minesweeper with restricted number
| Autor: | Wu, Ray Hua |
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| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Diplomová práce |
| Popis: | 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. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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