  Many applications, including rank aggregation and crowd-labeling, can be
modeled in terms of a bivariate isotonic matrix with unknown permutations
acting on its rows and columns. We consider the problem of estimating such a
matrix based on noisy observations of a subset of its entries, and design and
analyze a polynomial-time algorithm that improves upon the state of the art. In
particular, our results imply that any such $n \times n$ matrix can be
estimated efficiently in the normalized Frobenius norm at rate
$\widetilde{\mathcal O}(n^{-3/4})$, thus narrowing the gap between
$\widetilde{\mathcal O}(n^{-1})$ and $\widetilde{\mathcal O}(n^{-1/2})$, which
were hitherto the rates of the most statistically and computationally efficient
methods, respectively.
