Massively winning configurations in the convex grabbing game on the plane

Dvorak M, Nicholson S. 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.

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Conference Paper | Accepted | English
Author
Dvorak, MartinIST Austria ; Nicholson, Sara
Abstract
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.
Publishing Year
Date Published
2021-06-29
Proceedings Title
Proceedings of the 33rd Canadian Conference on Computational Geometry
Conference
CCCG: Canadian Conference on Computational Geometry
Conference Location
Halifax, NS, Canada
Conference Date
2021-08-10 – 2021-08-12
IST-REx-ID

Cite this

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.
Dvorak, M., & Nicholson, S. (n.d.). Massively winning configurations in the convex grabbing game on the plane. In Proceedings of the 33rd Canadian Conference on Computational Geometry. Halifax, NS, Canada.
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, n.d.
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.
Dvorak M, Nicholson S. 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.
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.
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2021-06-28
MD5 Checksum
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Access Level
OA Open Access
Date Uploaded
2021-08-12
MD5 Checksum
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