A Semi-streaming Algorithm for Monotone Regularized Submodular Maximization with a Matroid Constraint

In the face of large-scale datasets in many practical problems, it is an effective method to design approximation algorithms for maximizing a regularized submodular function in a semi-streaming model. In this paper, we study the monotone regularized submodular maximization with a matroid constraint and present a single-pass semi-streaming algorithm using multilinear extension function and greedy idea. We show that our algorithm has an approximation ratio of((beta-1)(1-e(-alpha))/beta+alpha beta-alpha, beta(beta-1)(1-e(-alpha))/beta+alpha beta-alpha)and amemory of O(r(M)), wherer(M)is the rank of the matroid and parameters alpha, beta >1.Specifically, if alpha=1.18 and beta=9.784, our algorithm is(0.302,2.955)-approximate.If alpha=1.257 and beta=3.669, our algorithm is(0.272 6,1)-approximate.