One‐pass streaming algorithm for monotone lattice submodular maximization subject to a cardinality constraint

Abstract

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 −1 k log k), and per-element query complexity O(𝜖 −2 log 2 k).