Conway’s fried potato problem: a (quadratic) algorithm leading to anoptimal division for convex polygons

• Antonio Cañete ^[1] ; Isabel Fernández ^[1] ; Alberto Márquez ^[1]
  1. [1] Universidad de Sevilla

     Universidad de Sevilla

     Sevilla, España

     
• Localización: Discrete Mathematics Days 2022 / coord. por Luis Felipe Tabera Alonso, 2022, ISBN 978-84-19024-02-2, págs. 71-76
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Conway’s fried potato problem is an optimization question with the following originalstatement [7]: given a convex body C in Rd, which is the division of C into n subsets,by means of n − 1 successive hyperplane cuts (that is, each cut divides only one previoussubset), minimizing the largest inradius of the subsets? This question was treated in a workby A. Bezdek and K. Bezdek [1], determining the optimal value and describing an optimaldivision for this problem in an implicit way. In this work, we focus on the family of convexpolygons, and provide an algorithm leading to the corresponding optimal value (which is ofquadratic order with respect to the number of sides of the polygon).