The Power of Randomness and Continuity in Submodular Optimization

2026-07-22

Submodularity is a fundamental mathematical notion that captures the concept of diminishing returns, and is prevalent in many areas of science and technology. From pollution detection and gang violence reduction, to active influence spreading in social networks (as recent controversial events suggest), submodular maximization directly affects multiple aspects of our daily lives. With a constantly growing number of real-world applications, it is no surprise that combinatorial maximization problems with a submodular objective have been the focus of intense theoretical and practical research for more than a decade. Unfortunately, many of the fundamental submodular maximization problems remain unresolved and lack fast and simple to implement algorithms that can be used in practice. A main reason for this state is that the current algorithmic toolkit used to solve submodular maximization problems is insufficient. This research proposal addresses the theoretical foundations of submodular maximization. Our overarching goal is to enrich the algorithmic toolkit and devise new algorithmic approaches that can be broadly applied to fundamental problems in submodular maximization and combinatorial optimization. A successful outcome of this research project will be a new theoretical algorithmic foundation for submodular maximization, that will enable us to completely resolve basic optimization problems and facilitate the design of fast and simple to implement algorithms that can be used in practice. The combination of the latter with ongoing practical research on the numerous uses of submodularity, could lead to a significant revolution in our ability to identify and solve the many real-world applications of submodular maximization.

Israel

2025-12-01