The Power of Randomization: Efficient and Effective Algorithms for Constrained Submodular Maximization

TL;DR

This paper introduces new randomized algorithms for constrained submodular maximization that outperform existing deterministic methods in approximation ratio and efficiency, with extensive empirical validation in data mining and social computing.

Contribution

The paper presents novel randomized algorithms that improve approximation ratios and computational efficiency for submodular maximization under complex constraints.

Findings

Algorithms outperform state-of-the-art in approximation ratio

Algorithms demonstrate superior utility in applications

Empirical results show improved efficiency

Abstract

Submodular optimization has numerous applications such as crowdsourcing and viral marketing. In this paper, we study the fundamental problem of non-negative submodular function maximization subject to a $k$-system constraint, which generalizes many other important constraints in submodular optimization such as cardinality constraint, matroid constraint, and $k$-extendible system constraint. The existing approaches for this problem achieve the best-known approximation ratio of $k+2\sqrt{k+2}+3$ (for a general submodular function) based on deterministic algorithmic frameworks. We propose several randomized algorithms that improve upon the state-of-the-art algorithms in terms of approximation ratio and time complexity, both under the non-adaptive setting and the adaptive setting. The empirical performance of our algorithms is extensively evaluated in several applications related to data mining and social computing, and the experimental results demonstrate the superiorities of our algorithms in terms of both utility and efficiency.