Edge Matching with Inequalities, Triangles, Unknown Shape, and Two Players
© 2020 Information Processing Society of Japan. We analyze the computational complexity of several new variants of edge-matching puzzles. First we analyze inequality (instead of equality) constraints between adjacent tiles, proving the problem NP-complete for strict inequalities but polynomial-time...
| Main Authors: | , , , , , , , , , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Information Processing Society of Japan
2022
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| Online Access: | https://hdl.handle.net/1721.1/143956 |
| _version_ | 1826196309950857216 |
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| author | Bosboom, Jeffrey Chen, Charlotte Chung, Lily Compton, Spencer Coulombe, Michael Demaine, Erik D Demaine, Martin L Filho, Ivan Tadeu Ferreira Antunes Hendrickson, Dylan Hesterberg, Adam Hsu, Calvin Hu, William Korten, Oliver Luo, Zhezheng Zhang, Lillian |
| author2 | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory |
| author_facet | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Bosboom, Jeffrey Chen, Charlotte Chung, Lily Compton, Spencer Coulombe, Michael Demaine, Erik D Demaine, Martin L Filho, Ivan Tadeu Ferreira Antunes Hendrickson, Dylan Hesterberg, Adam Hsu, Calvin Hu, William Korten, Oliver Luo, Zhezheng Zhang, Lillian |
| author_sort | Bosboom, Jeffrey |
| collection | MIT |
| description | © 2020 Information Processing Society of Japan. We analyze the computational complexity of several new variants of edge-matching puzzles. First we analyze inequality (instead of equality) constraints between adjacent tiles, proving the problem NP-complete for strict inequalities but polynomial-time solvable for nonstrict inequalities. Second we analyze three types of triangular edge matching, of which one is polynomial-time solvable and the other two are NP-complete; all three are #P-complete. Third we analyze the case where no target shape is specified and we merely want to place the (square) tiles so that edges match exactly; this problem is NP-complete. Fourth we consider four 2-player games based on 1×n edge matching, all four of which are PSPACE-complete. Most of our NP-hardness reductions are parsimonious, newly proving #P and ASP-completeness for, e.g., 1 × n edge matching. Along the way, we prove #P-and ASP-completeness of planar 3-regular directed Hamiltonicity; we provide linear-time algorithms to find antidirected and forbidden-transition Eulerian paths; and we characterize the complexity of new partizan variants of the Geography game on graphs. |
| first_indexed | 2024-09-23T10:24:33Z |
| format | Article |
| id | mit-1721.1/143956 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:24:33Z |
| publishDate | 2022 |
| publisher | Information Processing Society of Japan |
| record_format | dspace |
| spelling | mit-1721.1/1439562023-07-28T17:19:30Z Edge Matching with Inequalities, Triangles, Unknown Shape, and Two Players Bosboom, Jeffrey Chen, Charlotte Chung, Lily Compton, Spencer Coulombe, Michael Demaine, Erik D Demaine, Martin L Filho, Ivan Tadeu Ferreira Antunes Hendrickson, Dylan Hesterberg, Adam Hsu, Calvin Hu, William Korten, Oliver Luo, Zhezheng Zhang, Lillian Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory © 2020 Information Processing Society of Japan. We analyze the computational complexity of several new variants of edge-matching puzzles. First we analyze inequality (instead of equality) constraints between adjacent tiles, proving the problem NP-complete for strict inequalities but polynomial-time solvable for nonstrict inequalities. Second we analyze three types of triangular edge matching, of which one is polynomial-time solvable and the other two are NP-complete; all three are #P-complete. Third we analyze the case where no target shape is specified and we merely want to place the (square) tiles so that edges match exactly; this problem is NP-complete. Fourth we consider four 2-player games based on 1×n edge matching, all four of which are PSPACE-complete. Most of our NP-hardness reductions are parsimonious, newly proving #P and ASP-completeness for, e.g., 1 × n edge matching. Along the way, we prove #P-and ASP-completeness of planar 3-regular directed Hamiltonicity; we provide linear-time algorithms to find antidirected and forbidden-transition Eulerian paths; and we characterize the complexity of new partizan variants of the Geography game on graphs. 2022-07-22T14:10:08Z 2022-07-22T14:10:08Z 2020 2022-07-22T14:06:12Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/143956 Bosboom, Jeffrey, Chen, Charlotte, Chung, Lily, Compton, Spencer, Coulombe, Michael et al. 2020. "Edge Matching with Inequalities, Triangles, Unknown Shape, and Two Players." Journal of Information Processing, 28 (0). en 10.2197/IPSJJIP.28.987 Journal of Information Processing Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Information Processing Society of Japan arXiv |
| spellingShingle | Bosboom, Jeffrey Chen, Charlotte Chung, Lily Compton, Spencer Coulombe, Michael Demaine, Erik D Demaine, Martin L Filho, Ivan Tadeu Ferreira Antunes Hendrickson, Dylan Hesterberg, Adam Hsu, Calvin Hu, William Korten, Oliver Luo, Zhezheng Zhang, Lillian Edge Matching with Inequalities, Triangles, Unknown Shape, and Two Players |
| title | Edge Matching with Inequalities, Triangles, Unknown Shape, and Two Players |
| title_full | Edge Matching with Inequalities, Triangles, Unknown Shape, and Two Players |
| title_fullStr | Edge Matching with Inequalities, Triangles, Unknown Shape, and Two Players |
| title_full_unstemmed | Edge Matching with Inequalities, Triangles, Unknown Shape, and Two Players |
| title_short | Edge Matching with Inequalities, Triangles, Unknown Shape, and Two Players |
| title_sort | edge matching with inequalities triangles unknown shape and two players |
| url | https://hdl.handle.net/1721.1/143956 |
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