  This paper describes an efficient reduction of the learning problem of
ranking to binary classification. The reduction guarantees an average pairwise
misranking regret of at most that of the binary classifier regret, improving a
recent result of Balcan et al which only guarantees a factor of 2. Moreover,
our reduction applies to a broader class of ranking loss functions, admits a
simpler proof, and the expected running time complexity of our algorithm in
terms of number of calls to a classifier or preference function is improved
from $\Omega(n^2)$ to $O(n \log n)$. In addition, when the top $k$ ranked
elements only are required ($k \ll n$), as in many applications in information
extraction or search engines, the time complexity of our algorithm can be
further reduced to $O(k \log k + n)$. Our reduction and algorithm are thus
practical for realistic applications where the number of points to rank exceeds
several thousands. Much of our results also extend beyond the bipartite case
previously studied.
  Our rediction is a randomized one. To complement our result, we also derive
lower bounds on any deterministic reduction from binary (preference)
classification to ranking, implying that our use of a randomized reduction is
essentially necessary for the guarantees we provide.
