{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/156791"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/156791","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Max 2SAT-3, Net, Euclidea: Techniques and Results in Computational Inapproximability","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Luo, Victor"],"institution":"Massachusetts Institute of Technology","degree_name":"Master","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. 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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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["M.Eng."]},{"key":"dc:title","label":"Title","values":["Max 2SAT-3, Net, Euclidea: Techniques and Results in Computational Inapproximability"]}]}],"canonical_facts":{"dc:contributor.advisor":["Demaine, Erik D."],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science"],"dc:creator":["Luo, Victor"],"dc:date.accessioned":["2024-09-16T13:49:23Z"],"dc:date.available":["2024-09-16T13:49:23Z"],"dc:date.issued":["2024-05"],"dc:description.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."],"dc:description.degree":["M.Eng."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/156791"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","Copyright retained by author(s)"],"dc:rights.uri":["https://creativecommons.org/licenses/by-nc-nd/4.0/"],"dc:title":["Max 2SAT-3, Net, Euclidea: Techniques and Results in Computational Inapproximability"],"dc:type":["Thesis"],"thesis:degree_name":["Master","Master of Engineering in Electrical Engineering and Computer Science"]},"updated_at":"2026-07-22T22:22:09Z"}