A framework for visualizing hardness reductions to grid-based games
Name
1018309999-MIT.pdf
Description
Full printable version
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769.17 KB
Format
Adobe PDF
Checksum (MD5)
6aa0a785230189741ee9c3fea5028553
Author(s)
Shen, Jeffrey David
Advisor(s)
Erik Demaine.
Date Issued
2016
Publisher
Massachusetts Institute of Technology
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.
Description
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).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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