DASH: A Distributed and Parallelizable Algorithm for Size-Constrained Submodular Maximization
Keywords:CSO: Distributed CSP/Optimization, CSO: Constraint Optimization, CSO: Constraint Programming, CSO: Constraint Satisfaction, CSO: Other Foundations of Constraint Satisfaction & Optimization
AbstractMapReduce (MR) algorithms for maximizing monotone, submodular functions subject to a cardinality constraint (SMCC) are currently restricted to the use of the linear-adaptive (non-parallelizable) algorithm GREEDY. Low-adaptive algorithms do not satisfy the requirements of these distributed MR frameworks, thereby limiting their performance. We study the SMCC problem in a distributed setting and propose the first MR algorithms with sublinear adaptive complexity. Our algorithms, R-DASH, T-DASH and G-DASH provide 0.316 - ε, 3/8 - ε , and (1 - 1/e - ε) approximation ratios, respectively, with nearly optimal adaptive complexity and nearly linear time complexity. Additionally, we provide a framework to increase, under some mild assumptions, the maximum permissible cardinality constraint from O( n / ℓ^2) of prior MR algorithms to O( n / ℓ ), where n is the data size and ℓ is the number of machines; under a stronger condition on the objective function, we increase the maximum constraint value to n. Finally, we provide empirical evidence to demonstrate that our sublinear-adaptive, distributed algorithms provide orders of magnitude faster runtime compared to current state-of-the-art distributed algorithms.
How to Cite
Dey, T., Chen, Y., & Kuhnle, A. (2023). DASH: A Distributed and Parallelizable Algorithm for Size-Constrained Submodular Maximization. Proceedings of the AAAI Conference on Artificial Intelligence, 37(4), 3941-3948. https://doi.org/10.1609/aaai.v37i4.25508
AAAI Technical Track on Constraint Satisfaction and Optimization