2026-09-19T16:59:22Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1131652026-06-06T00:48:43Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Erik Demaine.
Shen, Jeffrey David
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2018-01-12T21:01:12Z
2018-01-12T21:01:12Z
2016
2016
http://hdl.handle.net/1721.1/113165
1018309999
Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016.
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 67-70).
Hardness proofs for grid-based games often use gadgets connected together to represent computational problems. We present an open-source framework to implement these reductions, producing actual game instances out of hard computational instances. Our framework first converts the input problem instance into a graph, then draws the graph in an integer grid (a kind of orthogonal graph drawing problem), and finally replaces nodes and edges in this layout with gadgets. To ensure that the final output is aligned, we use linear programming to constrain how gadgets connect. We apply this framework to Circuit SAT and use it to show examples of reductions to Akari and Minesweeper. Lastly, we describe possible future optimizations to the framework to make the output smaller and how to extend it for a wider variety of games.
by Jeffrey David Shen.
M.Eng.
70 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.
A framework for visualizing hardness reductions to grid-based games
Thesis
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<Abstract>Hardness proofs for grid-based games often use gadgets connected together to represent computational problems. We present an open-source framework to implement these reductions, producing actual game instances out of hard computational instances. Our framework first converts the input problem instance into a graph, then draws the graph in an integer grid (a kind of orthogonal graph drawing problem), and finally replaces nodes and edges in this layout with gadgets. To ensure that the final output is aligned, we use linear programming to constrain how gadgets connect. We apply this framework to Circuit SAT and use it to show examples of reductions to Akari and Minesweeper. Lastly, we describe possible future optimizations to the framework to make the output smaller and how to extend it for a wider variety of games.</Abstract>
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