DASH: A Distributed and Parallelizable Algorithm for Size-Constrained Submodular Maximization

MapReduce (MR) algorithms for maximizing monotone, submodular functions subject to a cardinality constraint (SMCC) are currently restricted the use of linear-adaptive (non-parallelizable) algorithm GREEDY. Low-adaptive do not satisfy requirements these distributed MR frameworks, thereby limiting their performance. We study SMCC problem in setting and propose first with sublinear adaptive complexity. Our algorithms, R-DASH, T-DASH G-DASH provide 0.316 - ε, 3/8 ε , (1 1/e ε) approximation ratios, respectively, nearly optimal complexity linear time Additionally, we framework increase, under some mild assumptions, maximum permissible from O( n / ℓ^2) prior ℓ ), where is data size number machines; stronger condition on objective function, increase value n. Finally, empirical evidence demonstrate that our sublinear-adaptive, orders magnitude faster runtime compared current state-of-the-art algorithms.