approximation algorithms for hierarchical location problems
We formulate and (approximately) solve hierarchical versions of two prototypical problems in discrete location theory, namely, the metric uncapacitated k -median and facility location problems. Our work yields new insights into hierarchical clustering, a widely used technique in data analysis. First, we show that every metric space admits a hierarchical clustering that is within a constant factor of optimal at every level of granularity with respect to the average (squared) distance objective. Second, we provide a natural solution to the leaf ordering problem encountered in the traditional dendrogram-based approach to the visualization of hierarchical clusterings.
discrete location theory hierarchical clustering