Order Distances and Split Systems

Abstract Given a pairwise distance D on the elements in finite set X , order Δ (D) is defined by first associating total preorder ≼ x to each ∈ based and then quantifying disagreement between these preorders. The can be useful relational analyses because using instead of may make such less sensitive small variations . Relatively little known about properties for general distances Indeed, nearly all previous work has focused understanding treelike that is, arises as shortest path tree with non-negative edge weights mapped into its vertex set. In this paper we study decomposed sums simpler called split-distances. Such generalize distances, have applications areas classification theory phylogenetics.