Algebraic solutions to multidimensional minimax location problems with Chebyshev distance

TL;DR

This paper presents an algebraic method for solving multidimensional minimax location problems using Chebyshev distance, leveraging eigenvalues of matrices within idempotent algebra to simplify the problem.

Contribution

It introduces a novel algebraic approach based on eigenvalue extremal properties to solve both constrained and unconstrained minimax location problems.

Findings

Eigenvalue-based solutions simplify problem evaluation

Method applies to multidimensional Chebyshev distance problems

Provides explicit algebraic solutions for location problems

Abstract

Multidimensional minimax single facility location problems with Chebyshev distance are examined within the framework of idempotent algebra. A new algebraic solution based on an extremal property of the eigenvalues of irreducible matrices is given. The solution reduces both unconstrained and constrained location problems to evaluation of the eigenvalue and eigenvectors of an appropriate matrix.