Paper by Martin L. Demaine

Reference:

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, and Lillian Zhang, “Edge Matching with Inequalities, Triangles, Unknown Shape, and Two Players”, Journal of Information Processing, volume 28, 2020, pages 987–1007.

Abstract:

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.

Comments:

This paper is available as arXiv:2002.03887 and from J-STAGE.

Length:

The paper is 23 pages.

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The paper is available in PDF (2448k).

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Related papers:

LessThanEdgeMatching_JCDCGGG2019 (Edge Matching with Inequalities, Triangles, Unknown Shape, and Two Players)