Efficient computation of axiomatic diversity on unrestricted distance matrices

Determine whether a diversity function satisfying monotonicity, uniqueness, and continuity can be computed efficiently on unrestricted symmetric distance matrices.

Background

Mironov and Prokhorenkova’s three axioms—monotonicity, uniqueness, and continuity—are formulated for general symmetric nonnegative distance matrices, without requiring Euclidean realizability. The paper establishes an efficiently computable axiomatic diversity measure only after restricting the input domain to Euclidean-realizable distance matrices.

The unrestricted computational question therefore remains unresolved: the paper does not determine whether any diversity function satisfying all three axioms admits an efficient algorithm on the full domain of symmetric distance matrices.