Paper by Martin L. Demaine
- 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.
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 paper is available as arXiv:2002.03887 and from J-STAGE.
- The paper is 23 pages.
- The paper is available in PDF (2448k).
- See information on file formats.
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- Related papers:
- LessThanEdgeMatching_JCDCGGG2019 (Edge Matching with Inequalities, Triangles, Unknown Shape, and Two Players)
See also other papers by Martin Demaine.
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