  Many applications require randomly sampling bipartite graphs with fixed
degrees, or randomly sampling incidence matrices with fixed row and column
sums. Although several sampling algorithms exist, the ``curveball'' algorithm
is the most efficient with an asymptotic time complexity of O(n log n), and has
been proven to sample uniformly at random. In this paper, we introduce the
``fastball'' algorithm, which adopts a similar approach but has an asymptotic
time complexity of O(n). We show that a C++ implementation of fastball randomly
samples large bipartite graphs with fixed degrees faster than curveball, and
illustrate the value of this faster algorithm in the context of the fixed
degree sequence model for backbone extraction.
