Six Points Suffice: How to Check for Metric Consistency

In many areas of data analysis, it is desirable to have tools at hand for analyzing the structure of distance tables—or, in more mathematical terms, of finite metric spaces. One such tool, known as split decomposition theory has proven particularly useful in this respect. The class of so-called totally decomposable metrics forms a cornerstone for this theory, and much work has been devoted to their study. Recently, it has become apparent that a particular subclass of these metrics, the consistent metrics, are also of fundamental importance. In this paper, we give a six-point characterization of consistent metrics amongst the totally decomposable ones.