Fast bicriteria streaming algorithms for submodular cover problem under noise models

Abstract

The Submodular Cover ($\mathrm{SC}$) problem has attracted the attention of researchers because of its wide variety of applications in many domains. Previous studies on this problem have focused on solving it under the assumption of a non-noise environment or using the greedy algorithm to solve it under noise. However, in some applications, the data is often large-scale and brings a noisy version, so the existing solutions are ineffective or not applicable to large and noisy data. Motivated by this phenomenon, we study the Submodular Cover under Noises ($\mathrm{SCN}$) problem and propose two efficient streaming algorithms, which provide a solution with theoretical bounds under two common noise models, multiplicative and additive noises. The experimental results indicate that our proposed algorithms not only provide the solution with a high objective function value but also outperform the state-of-the-art algorithm in terms of both the number of queries and the running time.