  We consider the problem of monotone, submodular maximization over a ground
set of size $n$ subject to cardinality constraint $k$. For this problem, we
introduce the first deterministic algorithms with linear time complexity; these
algorithms are streaming algorithms. Our single-pass algorithm obtains a
constant ratio in $\lceil n / c \rceil + c$ oracle queries, for any $c \ge 1$.
In addition, we propose a deterministic, multi-pass streaming algorithm with a
constant number of passes that achieves nearly the optimal ratio with linear
query and time complexities. We prove a lower bound that implies no
constant-factor approximation exists using $o(n)$ queries, even if queries to
infeasible sets are allowed. An empirical analysis demonstrates that our
algorithms require fewer queries (often substantially less than $n$) yet still
achieve better objective value than the current state-of-the-art algorithms,
including single-pass, multi-pass, and non-streaming algorithms.
