One‐pass streaming algorithm for monotone lattice submodular maximization subject to a cardinality constraint - Zhang, Zhenning; Guo, Longkun; Wang, Linyang; Zou, Juan (Concurrency and computation, 2023)
Summary In the article, we devise streaming algorithms for maximization of a monotone submodular function subject to a cardinality constraint on the integer lattice. Based on the observation that lattice submodularity is not equivalent to diminishing return submodularity on the integer lattice but rather a weaker condition, we propose a one‐pass streaming algorithm with a modified binary search as subroutine of each step. Finally, we show that the algorithm is with approximation ratio 1/2−ε, memory complexity O(ε−1klogk), and per‐element query complexity O(ε−2log2k).