Ultrametric location and parsimonious representation

Abstract

We consider single attractive facility location problems of general kind, with distance measured by an ultrametric. We show that the set of destinations always contains an (and often all) optimal solution(s), leading to an enumeration algorithm of at least quadratic space and time complexity, based on the matrix representation of the ultrametric. We then introduce a memory-efficient data structure to represent finite ultrametric spaces in linear space. Using this parsimonious representation most common location problems may be solved in linear or near-linear time.