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Different formulations of the gray pattern problem and their optimal solutions

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  • Brimberg, Jack
  • Kalczynski, Pawel
  • Drezner, Zvi

Abstract

The Gray Pattern Problem (GPP) requires selecting a given number (p) of pixels (or dots) within a central rectangle to be colored black (the remaining pixels remain white) to form a repeating pattern covering the plane that is as uniformly gray as possible. Taillard proposed the original model in 1995, which is based on the principle of minimization of entropy taken from physics. The aim of this paper is to present alternate formulations of the GPP inspired by dispersion models studied in location theory. We show that these variants have much greater tractability than the original model, while producing patterns of equivalent or better quality.

Suggested Citation

  • Brimberg, Jack & Kalczynski, Pawel & Drezner, Zvi, 2024. "Different formulations of the gray pattern problem and their optimal solutions," European Journal of Operational Research, Elsevier, vol. 316(1), pages 61-71.
    • Handle: RePEc:eee:ejores:v:316:y:2024:i:1:p:61-71
    DOI: 10.1016/j.ejor.2024.01.048
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