Parametric Streaming Two-Stage Submodular Maximization - Yang, Ruiqi; Xu, Dachuan; Guo, Longkun; Zhang, Dongmei (Theory and Applications of Models of Computation, 2020)
We study the submodular maximization problem in generalized streaming setting using a two-stage policy. In the streaming context, elements are released in a fashion that an element is revealed at one time. Subject to a limited memory capacity, the problem aims to sieve a subset of elements with a sublinear size $$\ell $$ , such that the expecting objective value of all utility functions over the summarized subsets has a performance guarantee. We present a generalized one pass, $$\left( γ ^5_{\min }/(5+ 2γ ^2_{\min } )-O(ε )\right) $$ -approximation, which consumes $$O(ε ^{-1}\ell \log (\ell γ _{\min }^{-1}))$$ memory and runs in $$O(ε ^{-1}kmn\log (\ell γ _{\min }^{-1}))$$ time, where k, n, m and $$γ _{\min }$$ denote the cardinality constraint, the element stream size, the amount of the learned functions, and the minimum generic submodular ratio of the learned functions, respectively.