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Everything about Polymatroid
Multiset analogue of matroids
In mathematics, a polymatroid is a polytope associated with a submodular function. The notion was introduced by Jack Edmonds in 1970. It is also a generalization of the notion of a matroid. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: PolymatroidA 5-minute orientation
- Skim a recent paper: The Natural Matroid of an Integer PolymatroidInfluential work since 2022
- Pick up a classic book: Conservation laws, extended polymatroids and multi-armed bandit problemsThe most-reprinted book on the subject
- Read the landmark paper: Multiaccess fading channels. I. Polymatroid structure, optimal resource allocation and throughput capacitiesCited 801 times
- Go sideways: Matroid polytopeA closely related topic
- Go sideways: Submodular set functionA closely related topic
📖 Definitions
Noun A particular form of polytope
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Multiaccess fading channels. I. Polymatroid structure, optimal resource allocation and throughput capacities
M-Convex Function on Generalized Polymatroid
Lexicographically Optimal Base of a Polymatroid with Respect to a Weight Vector
Integer Rounding for Polymatroid and Branching Optimization Problems
Two algorithms for maximizing a separable concave function over a polymatroid feasible region
The Partial Order of a Polymatroid Extreme Point
Polymatroid Optimization, Submodularity, and Joint Replenishment Games
The Polymatroid Steiner Problems
🆕 Influential since 2022
📚 Books worth reading
Conservation laws, extended polymatroids and multi-armed bandit problemsDimitris Bertsimas · 1993- 📕Ganzzahlige Polymatroid-Intersektions-AlgorithmenPaul Schönsleben · 1980
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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