Diversity maximization is an important concept in information retrieval,
computational geometry and operations research. Usually, it is a variant of the
following problem: Given a ground set, constraints, and a function f(â‹…)
that measures diversity of a subset, the task is to select a feasible subset
S such that f(S) is maximized. The \emph{sum-dispersion} function f(S)=∑x,y∈S​d(x,y), which is the sum of the pairwise distances in S, is
in this context a prominent diversification measure. The corresponding
diversity maximization is the \emph{max-sum} or \emph{sum-sum diversification}.
Many recent results deal with the design of constant-factor approximation
algorithms of diversification problems involving sum-dispersion function under
a matroid constraint. In this paper, we present a PTAS for the max-sum
diversification problem under a matroid constraint for distances
d(â‹…,â‹…) of \emph{negative type}. Distances of negative type are, for
example, metric distances stemming from the ℓ2​ and ℓ1​ norm, as well
as the cosine or spherical, or Jaccard distance which are popular similarity
metrics in web and image search