Vol. 15, No. 1, 2022

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Applying iterated mapping to the no-three-in-a-line problem

Cole Brower and Vadim Ponomarenko

Vol. 15 (2022), No. 1, 69–74
Abstract

Iterated mapping has seen a lot of success lately in many problems such as bit retrieval, diffraction signal reconstruction, and graph coloring. We add another application of iterated mapping, namely finding solutions to the no-three-in-a-line problem. Given an n × n grid, we utilize iterated mapping to find 2n points such that any straight line (of any slope) drawn will not intersect three of the selected points.

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Keywords
combinatorial search, no-three-in-a-line, global optimization
Mathematical Subject Classification
Primary: 05-04, 11Y16, 52B55
Milestones
Received: 15 September 2020
Revised: 14 July 2021
Accepted: 12 August 2021
Published: 14 March 2022

Communicated by Kenneth S. Berenhaut
Authors
Cole Brower
Department of Mathematics and Statistics
San Diego State University
San Diego, CA
United States
Vadim Ponomarenko
Department of Mathematics and Statistics
San Diego State University
San Diego, CA
United States