# Submodular Optimization Over Streams with Inhomogeneous Decays

arXiv: https://arxiv.org/abs/1811.05652 · HTML: https://mlsanity.com/paper/1811.05652/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Nov 2018.

## Built on by (most cited first, 2 of 2)

- [Deletion Robust Submodular Maximization over Matroids](https://mlsanity.com/paper/2201.13128/) (2022)
- [Deletion Robust Non-Monotone Submodular Maximization over Matroids](https://mlsanity.com/paper/2208.07582/) (2022)

## Abstract (arXiv)

Cardinality constrained submodular function maximization, which aims to select a subset of size at most k to maximize a monotone submodular utility function, is the key in many data mining and machine learning applications such as data summarization and maximum coverage problems. When data is given as a stream, streaming submodular optimization (SSO) techniques are desired. Existing SSO techniques can only apply to insertion-only streams where each element has an infinite lifespan, and sliding-window streams where each element has a same lifespan (i.e., window size). However, elements in some data streams may have arbitrary different lifespans, and this requires addressing SSO over streams with inhomogeneous-decays (SSO-ID). This work formulates the SSO-ID problem and presents three algorithms: BasicStreaming is a basic streaming algorithm that achieves an (1/2-ε) approximation factor; HistApprox improves the efficiency significantly and achieves an (1/3-ε) approximation factor; HistStreaming is a streaming version of HistApprox and uses heuristics to further improve the efficiency. Experiments conducted on real data demonstrate that HistStreaming can find high quality solutions and is up to two orders of magnitude faster than the naive Greedy algorithm.