Max 2SAT-3, Net, Euclidea: Techniques and Results in Computational Inapproximability
Name
luo-vluo-meng-eecs-2024-thesis.pdf
Description
Thesis PDF
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1.03 MB
Format
Adobe PDF
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Author(s)
Luo, Victor
Advisor(s)
Demaine, Erik D.
Date Issued
May 2024
Publisher
Massachusetts Institute of Technology
Abstract
This Master’s thesis investigates three diverse problem domains through the lens of computational inapproximability: Max 2SAT-3, the Net tile-rotating puzzle family, and the mobile game Euclidea. Max 2SAT-3 is a problem long known to be APX-complete, but finding a clear proof is harder than one might expect. We examine the history of Max 2SAT-3, addressing past misconceptions and clarifying where the reduction chain has been opaque, and present a novel proof of its APX-completeness. Net variants form a wide class of puzzles with lots of potential for future research. We introduce a natural optimization variant of Net and demonstrate its inapproximability, as well as consolidate existing findings and present other new results. Euclidea is a mobile game based on Euclidean straightedge-and-compass constructions. We define the game as an optimization problem and establish its APX-hardness, as well as discuss challenges in upper-bounding its complexity, relating to current knowledge gaps regarding the constructible and algebraic numbers.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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