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

Brower, Cole; Ponomarenko, Vadim

doi:10.2140/involve.2022.15.69

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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

DOI: 10.2140/involve.2022.15.69

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 $n \times n$ grid, we utilize iterated mapping to find $2 n$ points such that any straight line (of any slope) drawn will not intersect three of the selected points.

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

Vol. 15, No. 1, 2022