  In this work, we present a combinatorial, deterministic single-pass streaming
algorithm for the problem of maximizing a submodular function, not necessarily
monotone, with respect to a cardinality constraint (SMCC). In the case the
function is monotone, our algorithm reduces to the optimal streaming algorithm
of Badanidiyuru et al. (2014). In general, our algorithm achieves ratio $\alpha
/ (1 + \alpha) - \varepsilon$, for any $\varepsilon > 0$, where $\alpha$ is the
ratio of an offline (deterministic) algorithm for SMCC used for
post-processing. Thus, if exponential computation time is allowed, our
algorithm deterministically achieves nearly the optimal $1/2$ ratio. These
results nearly match those of a recently proposed, randomized streaming
algorithm that achieves the same ratios in expectation. For a deterministic,
single-pass streaming algorithm, our algorithm achieves in polynomial time an
improvement of the best approximation factor from $1/9$ of previous literature
to $\approx 0.2689$.
