  Motivated by applications in recommender systems, web search, social choice
and crowdsourcing, we consider the problem of identifying the set of top $K$
items from noisy pairwise comparisons. In our setting, we are non-actively
given $r$ pairwise comparisons between each pair of $n$ items, where each
comparison has noise constrained by a very general noise model called the
strong stochastic transitivity (SST) model. We analyze the competitive ratio of
algorithms for the top-$K$ problem. In particular, we present a linear time
algorithm for the top-$K$ problem which has a competitive ratio of
$\tilde{O}(\sqrt{n})$; i.e. to solve any instance of top-$K$, our algorithm
needs at most $\tilde{O}(\sqrt{n})$ times as many samples needed as the best
possible algorithm for that instance (in contrast, all previous known
algorithms for the top-$K$ problem have competitive ratios of
$\tilde{\Omega}(n)$ or worse). We further show that this is tight: any
algorithm for the top-$K$ problem has competitive ratio at least
$\tilde{\Omega}(\sqrt{n})$.
