  Pairwise comparison labels are more informative and less variable than class
labels, but generating them poses a challenge: their number grows quadratically
in the dataset size. We study a natural experimental design objective, namely,
D-optimality, that can be used to identify which $K$ pairwise comparisons to
generate. This objective is known to perform well in practice, and is
submodular, making the selection approximable via the greedy algorithm. A
na\"ive greedy implementation has $O(N^2d^2K)$ complexity, where $N$ is the
dataset size, $d$ is the feature space dimension, and $K$ is the number of
generated comparisons. We show that, by exploiting the inherent geometry of the
dataset--namely, that it consists of pairwise comparisons--the greedy
algorithm's complexity can be reduced to $O(N^2(K+d)+N(dK+d^2) +d^2K).$ We
apply the same acceleration also to the so-called lazy greedy algorithm. When
combined, the above improvements lead to an execution time of less than 1 hour
for a dataset with $10^8$ comparisons; the na\"ive greedy algorithm on the same
dataset would require more than 10 days to terminate.
