Simultaenous Sieves: A Deterministic Streaming Algorithm for Non-Monotone Submodular Maximization · arXivDesk
2010.14367Oct 27, 2020Withdrawn as essentially the same deterministic algorithm, with the same ratio, was developed in the journal version of the paper: Alaluf et al. Optimal Streaming Algorithms for Submodular Maximization with Cardinality Constraints, submitted to Mathematics of Operations Research
Simultaenous Sieves: A Deterministic Streaming Algorithm for Non-Monotone Submodular Maximization
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 α/(1+α)−ε, for any ε>0, where α
Nearby in the stack
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