Criteria for Polynomial Time (

Research in cluster analysis has resulted in a large number of algorithms and similarity measurements for clustering scienti c data. Machine learning researchers have published a number of methods for conceptual clustering, in which observations are grouped into clusters which have \good" descriptions in some language. We investigate the general properties which similarity metrics, objective functions, and concept description languages must have to guarantee that a (conceptual) clustering problem is polynomial time solvable by a simple and widely-used clustering technique, the agglomerative-hierarchical algorithm. We show that under fairly general conditions, the agglomerative-hierarchical method may be used to nd an optimal solution in polynomial time.