Series
Submodular Maximization in Practice
A practical series on submodular maximization, from intuition and formal definitions to scalable greedy algorithms.
An Introduction to Submodularity
A practical introduction to submodular functions, the mathematical framework behind diminishing returns, covering set functions, marginal gains, and real-world applications from sensor placement to influence maximization.
The Greedy Algorithm for Submodular Maximization
The greedy algorithm achieves a (1 - 1/e) approximation for monotone submodular maximization, provably the best any efficient algorithm can do. This post covers the algorithm, its proof, Lazy Greedy, and when greedy fails.
Stochastic Greedy: Scaling Submodular Maximization to Massive Datasets
Stochastic Greedy replaces greedy's full scan with random subsampling, reducing runtime from O(nk) to O(n log(1/ε)) while losing only an additive ε in the approximation guarantee. This post covers the algorithm, its proof, and practical guidance.