| Item type |
Journal(1) |
| 公開日 |
2020-12-15 |
| タイトル |
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タイトル |
Edge Matching with Inequalities, Triangles, Unknown Shape, and Two Players |
| タイトル |
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言語 |
en |
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タイトル |
Edge Matching with Inequalities, Triangles, Unknown Shape, and Two Players |
| 言語 |
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言語 |
eng |
| キーワード |
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主題Scheme |
Other |
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主題 |
[特集：離散と計算の幾何・グラフ・ゲーム] complexity, puzzles and games, satisfiability, Hamiltonicity, Eulerian paths, Geography |
| 資源タイプ |
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資源タイプ識別子 |
http://purl.org/coar/resource_type/c_6501 |
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資源タイプ |
journal article |
| 著者所属 |
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MIT Computer Science and Artificial Intelligence Laboratory |
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MIT Computer Science and Artificial Intelligence Laboratory |
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MIT Computer Science and Artificial Intelligence Laboratory |
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MIT Computer Science and Artificial Intelligence Laboratory |
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MIT Computer Science and Artificial Intelligence Laboratory |
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MIT Computer Science and Artificial Intelligence Laboratory |
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MIT Computer Science and Artificial Intelligence Laboratory |
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MIT Computer Science and Artificial Intelligence Laboratory |
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MIT Computer Science and Artificial Intelligence Laboratory |
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MIT Computer Science and Artificial Intelligence Laboratory |
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MIT Computer Science and Artificial Intelligence Laboratory |
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MIT Computer Science and Artificial Intelligence Laboratory |
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Department of Computer Science, Tufts University |
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MIT Computer Science and Artificial Intelligence Laboratory |
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MIT Computer Science and Artificial Intelligence Laboratory |
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en |
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MIT Computer Science and Artificial Intelligence Laboratory |
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en |
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MIT Computer Science and Artificial Intelligence Laboratory |
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en |
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MIT Computer Science and Artificial Intelligence Laboratory |
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en |
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MIT Computer Science and Artificial Intelligence Laboratory |
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en |
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MIT Computer Science and Artificial Intelligence Laboratory |
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en |
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MIT Computer Science and Artificial Intelligence Laboratory |
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en |
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MIT Computer Science and Artificial Intelligence Laboratory |
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en |
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MIT Computer Science and Artificial Intelligence Laboratory |
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en |
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MIT Computer Science and Artificial Intelligence Laboratory |
| 著者所属(英) |
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en |
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MIT Computer Science and Artificial Intelligence Laboratory |
| 著者所属(英) |
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en |
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MIT Computer Science and Artificial Intelligence Laboratory |
| 著者所属(英) |
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en |
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MIT Computer Science and Artificial Intelligence Laboratory |
| 著者所属(英) |
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en |
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Department of Computer Science, Tufts University |
| 著者所属(英) |
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en |
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MIT Computer Science and Artificial Intelligence Laboratory |
| 著者所属(英) |
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en |
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MIT Computer Science and Artificial Intelligence Laboratory |
| 著者名 |
Jeffrey, Bosboom
Charlotte, Chen
Lily, Chung
Spencer, Compton
Michael, Coulombe
Erik, D. Demaine
Martin, L. Demaine
Ivan, Tadeu Ferreira Antunes Filho
Dylan, Hendrickson
Adam, Hesterberg
Calvin, Hsu
William, Hu
Oliver, Korten
Zhezheng, Luo
Lillian, Zhang
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| 著者名(英) |
Jeffrey, Bosboom
Charlotte, Chen
Lily, Chung
Spencer, Compton
Michael, Coulombe
Erik, D. Demaine
Martin, L. Demaine
Ivan, Tadeu Ferreira Antunes Filho
Dylan, Hendrickson
Adam, Hesterberg
Calvin, Hsu
William, Hu
Oliver, Korten
Zhezheng, Luo
Lillian, Zhang
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| 論文抄録 |
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内容記述タイプ |
Other |
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内容記述 |
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.
------------------------------
This is a preprint of an article intended for publication Journal of
Information Processing(JIP). This preprint should not be cited. This
article should be cited as: Journal of Information Processing Vol.28(2020) (online)
DOI http://dx.doi.org/10.2197/ipsjjip.28.987
------------------------------ |
| 論文抄録(英) |
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内容記述タイプ |
Other |
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内容記述 |
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.
------------------------------
This is a preprint of an article intended for publication Journal of
Information Processing(JIP). This preprint should not be cited. This
article should be cited as: Journal of Information Processing Vol.28(2020) (online)
DOI http://dx.doi.org/10.2197/ipsjjip.28.987
------------------------------ |
| 書誌レコードID |
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収録物識別子タイプ |
NCID |
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収録物識別子 |
AN00116647 |
| 書誌情報 |
情報処理学会論文誌
巻 61,
号 12,
発行日 2020-12-15
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| ISSN |
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収録物識別子タイプ |
ISSN |
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収録物識別子 |
1882-7764 |
IPSJ-JNL6112029.pdf (2.2 MB)
