New geometrical compactness measures for zones design

• Main Authors: Eric Alfredo Rincón-García, Miguel Ángel Gutiérrez Andrade, Sergio Gerardo de los Cobos Silva, Pedro Lara Velázquez
• Format: Article
• Language: Spanish
• Published: Universidad de Costa Rica 2012-07-01
• Series: Revista de Matemática: Teoría y Aplicaciones
• Online Access: https://revistas.ucr.ac.cr/index.php/matematica/article/view/1333

The design of compact zones has been studied because of its influence in the creation of zones with regular forms, which are easier to analyze, to investigate or to administer. This paper propose a new method to measure compactness,by means of the transformation of the original geographical spaces, into figures formed with square cells, which are used to measure the similarity between the original zone and an ideal zone with straight forms. The proposed method was applied to design electoral zones, which must satisfy constraints of compactness, contiguity and population balance, in a topographical configuration that favors the creation of twisted and diffuse shapes. The results show that the new method favors the creation of zones with straight forms, without an important effect to the population balance, which are considered zones of high quality. Keywords: Redistricting, compactness, simulated annealing, GIS. Mathematics Subject Classification: 90C59, 90C29, 68T20.