Parametric Streaming Two-Stage Submodular Maximization

• Published in: Theory and Applications of Models of Computation Vol. 12337; pp. 193 - 204
• Main Authors: Yang, Ruiqi, Xu, Dachuan, Guo, Longkun, Zhang, Dongmei
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2020; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Approximation ratio; Streaming algorithm; Submodular maximization; Submodular ratio
• ISBN: 3030592669; 9783030592660
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-59267-7_17

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, $$\left( \gamma ^5_{\min }/(5+ 2\gamma ^2_{\min } )-O(\epsilon )\right) $$ -approximation, which consumes $$O(\epsilon ^{-1}\ell \log (\ell \gamma _{\min }^{-1}))$$ memory and runs in $$O(\epsilon ^{-1}kmn\log (\ell \gamma _{\min }^{-1}))$$ time, where k, n, m and $$\gamma _{\min }$$ 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.