Everything about Submodular set function
Set-to-real map with diminishing returns
In mathematics, a submodular set function is a set function that, informally, describes the relationship between a set of inputs and an output, where adding more of one input has a decreasing additional benefit. The natural diminishing returns property which makes them suitable for many applications, including approximation algorithms, game theory and electrical networks. Recently, submodular functions have also found utility in several real world problems in machine learning and artificial intelligence, including automatic summarization, multi-document summarization, feature selection, active learning, sensor placement, image collection summarization and many other domains. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Submodular set functionA 5-minute orientation
- Skim a recent paper: Monotonic Decompositions of Submodular Set FunctionsInfluential work since 2022
- Pick up a classic book: Mathematical programming at Oberwolfach IIThe most-reprinted book on the subject
- Read the landmark paper: An analysis of approximations for maximizing submodular set functions—ICited 3,178 times
- Go sideways: Subadditive set functionA closely related topic
- Go sideways: PolymatroidA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
An analysis of approximations for maximizing submodular set functions—I
A note on maximizing a submodular set function subject to a knapsack constraint
Best Algorithms for Approximating the Maximum of a Submodular Set Function
Maximizing Submodular Set Function With Connectivity Constraint: Theory and Application to Networks
A Mazur-Orlicz type theorem for submodular set functions
Approximation Algorithms for Stochastic Submodular Set Cover with Applications to Boolean Function Evaluation and Min-Knapsack
Rigid Network Design Via Submodular Set Function Optimization
Distributed strategy selection: A submodular set function maximization approach
🆕 Influential since 2022
đź“š Books worth reading
Mathematical programming at Oberwolfach IIB. H. Korte, M. L. Balinski · 1984
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
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