In this work we consider the diversity maximization problem, where given a
data set X of n elements, and a parameter k, the goal is to pick a subset
of X of size k maximizing a certain diversity measure. [CH01] defined a
variety of diversity measures based on pairwise distances between the points. A
constant factor approximation algorithm was known for all those diversity
measures except ``remote-matching'', where only an O(logk) approximation
was known. In this work we present an O(1) approximation for this remaining
notion. Further, we consider these notions from the perpective of composable
coresets. [IMMM14] provided composable coresets with a constant factor
approximation for all but ``remote-pseudoforest'' and ``remote-matching'',
which again they only obtained a O(logk) approximation. Here we also close
the gap up to constants and present a constant factor composable coreset
algorithm for these two notions. For remote-matching, our coreset has size only
O(k), and for remote-pseudoforest, our coreset has size
O(k1+ε) for any ε>0, for an
O(1/ε)-approximate coreset.Comment: 27 pages, 1 table. Accepted to APPROX, 202