Massively winning configurations in the convex grabbing game on the plane

conference paper Massively winning configurations in the convex grabbing game on the plane published yes Martin Dvorak author 40ED02A8-C8B4-11E9-A9C0-453BE66974250000-0001-5293-214X Sara Nicholson author GradSch department VlKo department CCCG: Canadian Conference on Computational Geometry The convex grabbing game is a game where two players, Alice and Bob, alternate taking extremal points from the convex hull of a point set on the plane. Rational weights are given to the points. The goal of each player is to maximize the total weight over all points that they obtain. We restrict the setting to the case of binary weights. We show a construction of an arbitrarily large odd-sized point set that allows Bob to obtain almost 3/4 of the total weight. This construction answers a question asked by Matsumoto, Nakamigawa, and Sakuma in [Graphs and Combinatorics, 36/1 (2020)]. We also present an arbitrarily large even-sized point set where Bob can obtain the entirety of the total weight. Finally, we discuss conjectures about optimum moves in the convex grabbing game for both players in general. https://research-explorer.ista.ac.at/download/9592/9616/Convex-Grabbing-Game_CCCG_proc_version.pdf application/pdfno https://research-explorer.ista.ac.at/download/9592/9902/Convex-Grabbing-Game_FULL-VERSION.pdf application/pdfno https://creativecommons.org/licenses/by-nd/4.0/ Canadian Conference on Computational Geometry2021Halifax, NS, Canada; Virtual eng convex grabbing gamegraph grabbing gamecombinatorial gameconvex geometry Proceedings of the 33rd Canadian Conference on Computational Geometry 2106.11247 M. Dvorak and S. Nicholson, “Massively winning configurations in the convex grabbing game on the plane,” in Proceedings of the 33rd Canadian Conference on Computational Geometry, Halifax, NS, Canada; Virtual, 2021. M. Dvorak, S. Nicholson, in:, Proceedings of the 33rd Canadian Conference on Computational Geometry, Canadian Conference on Computational Geometry, 2021. Dvorak, Martin, and Sara Nicholson. “Massively Winning Configurations in the Convex Grabbing Game on the Plane.” Proceedings of the 33rd Canadian Conference on Computational Geometry, Canadian Conference on Computational Geometry, 2021. Dvorak, M., & Nicholson, S. (2021). Massively winning configurations in the convex grabbing game on the plane. In Proceedings of the 33rd Canadian Conference on Computational Geometry. Halifax, NS, Canada; Virtual: Canadian Conference on Computational Geometry. Dvorak, Martin, and Sara Nicholson. “Massively Winning Configurations in the Convex Grabbing Game on the Plane.” In Proceedings of the 33rd Canadian Conference on Computational Geometry. Canadian Conference on Computational Geometry, 2021. Dvorak M, Nicholson S. Massively winning configurations in the convex grabbing game on the plane. In: Proceedings of the 33rd Canadian Conference on Computational Geometry. Canadian Conference on Computational Geometry; 2021. Dvorak M, Nicholson S. 2021. Massively winning configurations in the convex grabbing game on the plane. Proceedings of the 33rd Canadian Conference on Computational Geometry. CCCG: Canadian Conference on Computational Geometry. 95922021-06-22T15:57:11Z2025-05-14T11:23:45Z