A Majority Theorem for the Uncapacitated p = 2 Median Problem and Local Spatial Autocorrelation

• Published in: Mathematics (Basel) Vol. 13; no. 2; p. 249
• Main Authors: Griffith, Daniel A., Chun, Yongwan, Kim, Hyun
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.01.2025
• Subjects: Algorithms; Autocorrelation; Geographical distribution; Geospatial data; local spatial autocorrelation; majority theorem; Operations research; Optimization; spatial autocorrelation; spatial median; spatial optimization; Statistics; Theorems; United States
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math13020249

The existing quantitative geography literature contains a dearth of articles that span spatial autocorrelation (SA), a fundamental property of georeferenced data, and spatial optimization, a popular form of geographic analysis. The well-known location–allocation problem illustrates this state of affairs, although its empirical geographic distribution of demand virtually always exhibits positive SA. This latent redundant attribute information alludes to other tools that may well help to solve such spatial optimization problems in an improved, if not better than, heuristic way. Within a proof-of-concept perspective, this paper articulates connections between extensions of the renowned Majority Theorem of the minisum problem and especially the local indices of SA (LISA). The relationship articulation outlined here extends to the p = 2 setting linkages already established for the p = 1 spatial median problem. In addition, this paper presents the foundation for a novel extremely efficient p = 2 algorithm whose formulation demonstratively exploits spatial autocorrelation.