Geometrical Solutions for Some Minimax Location Problems

1972/11/01 by Jack Elzinga, Donald W. Hearn · 347 citations
Business, Management and Accounting · Computer Science · Mathematics · #Facility Location and Emergency Management #Computational Geometry and Mesh Generation #Optimization and Variational Analysis #Minimax #Point (geometry) #Mathematical optimization #Euclidean distance #Plane (geometry) #Euclidean geometry #Mathematics #1-center problem #Finite set #Set (abstract data type) #Constant (computer programming) #Facility location problem #Applied mathematics #Computer science #Geometry #Mathematical analysis

paper · doi:10.1287/trsc.6.4.379

published in Transportation Science 6(4), 379-394 (Institute for Operations Research and the Management Sciences)

openalex publication_date 1972/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11

Abstract

Four closely related minimax location problems are considered. Each involves locating a point in the plane to minimize the maximum distance (plus a possible constant) to a given finite set of points. The distance measures considered are the Euclidean and the rectilinear. In each case efficient, finite solution procedures are given. The arguments are geometrical.

Citations

• The Minimum Covering Sphere Problem

Cited by

• Efficient Algorithms for the (Weighted) Minimum Circle Problem
• The Weighted Euclidean 1-Center Problem
• Minimax Multifacility Location with Euclidean Distances
• On the Complexity of the Elzinga-Hearn Algorithm for the 1-Center Problem
• Letter to the Editor—Note on Geometrical Solution for Some Minimax Location Problems
• Linear-Time Algorithms for Linear Programming in R³ and Related Problems
• Smallest-circle problem [wikipedia]