# Submodularity on Hypergraphs: From Sets to Sequences

arXiv: https://arxiv.org/abs/1802.09110 · HTML: https://mlsanity.com/paper/1802.09110/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2018.

## Built on by (most cited first, 3 of 3)

- [Tokenized Bandit for LLM Decoding and Alignment](https://mlsanity.com/paper/2506.07276/) (2025)
- [Multi-objective Evolutionary Algorithms are Generally Good: Maximizing Monotone Submodular Functions over Sequences](https://mlsanity.com/paper/2104.09884/) (2021)
- [Robust Sequence Networked Submodular Maximization](https://mlsanity.com/paper/2212.13725/) (2022)

## Abstract (arXiv)

In a nutshell, submodular functions encode an intuitive notion of diminishing returns. As a result, submodularity appears in many important machine learning tasks such as feature selection and data summarization. Although there has been a large volume of work devoted to the study of submodular functions in recent years, the vast majority of this work has been focused on algorithms that output sets, not sequences. However, in many settings, the order in which we output items can be just as important as the items themselves. To extend the notion of submodularity to sequences, we use a directed graph on the items where the edges encode the additional value of selecting items in a particular order. Existing theory is limited to the case where this underlying graph is a directed acyclic graph. In this paper, we introduce two new algorithms that provably give constant factor approximations for general graphs and hypergraphs having bounded in or out degrees. Furthermore, we show the utility of our new algorithms for real-world applications in movie recommendation, online link prediction, and the design of course sequences for MOOCs.