Single-Player and Two-Player Buttons & Scissors Games

We study the computational complexity of the Buttons \& Scissors game and obtain sharp thresholds with respect to several parameters. Specifically we show that the game is NP-complete for $C = 2$ colors but polytime solvable for $C = 1$. Similarly the game is NP-complete if every color is used by at most $F = 4$ buttons but polytime solvable for $F \leq 3$. We also consider restrictions on the board size, cut directions, and cut sizes. Finally, we introduce several natural two-player versions of the game and show that they are PSPACE-complete.Comment: 21 pages, 15 figures. Presented at JCDCG2 2015, Kyoto University, Kyoto, Japan, September 14 - 16, 201

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Problems presented at the open-problem session of the 14th Annual ACM Symposium on Computational Geometry are listed

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The subquadratic algorithm of Kapoor for finding shortest paths on a polyhedron is described

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The algorithm of Edelsbrunner for surface reconstruction by ``wrapping'' a set of points in R^3 is described.Comment: 4 pages, to appear in SIGACT News and in IJCGA, 200

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The recent result that n congruent balls in R^d have at most 4 distinct geometric permutations is described.Comment: To appear in SIGACT News and in Internat. J. Comput. Geom. App

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The concept of pointed pseudo-triangulations is defined and a few of its applications described.Comment: 3 pages, 1 figur

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A compendium of thirty previously published open problems in computational geometry is presented.Comment: 7 pages; 72 reference

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The resolution of a decades-old open problem is described: polygonal chains cannot lock in the plane.Comment: 4 pages, 2 figures. To appear in SIGACT News and in Int. J. Comp. Geom. App

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Recent results on curve reconstruction are described.Comment: 3 pages, 1 figure, 18 ref