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Everything about Matroid parity problem
Largest independent set of paired elements
In combinatorial optimization, the matroid parity problem is a problem of finding the largest independent set of paired elements in a matroid, a structure that abstracts and generalizes the notion of linear independence in vector spaces. The problem was formulated by Lawler (1976) as a common generalization of graph matching and matroid intersection. It is also known as polymatroid matching, or the matchoid problem. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Matroid parity problemA 5-minute orientation
- Read the landmark paper: New algorithms for lineark-matroid intersection and matroidk-parity problemsCited 24 times
- Go sideways: PseudoforestA closely related topic
- Go sideways: Rigidity matroidA closely related topic
📖 Definitions
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🗂️ The subject at a glance
🏆 Landmark papers (most cited)
New algorithms for lineark-matroid intersection and matroidk-parity problems
Solving the linear matroid parity problem as a sequence of matroid intersection problems
The linear delta-matroid parity problem
Algebraic Algorithms for Linear Matroid Parity Problems
Heuristically guided algorithm for k-parity matroid problems
On the graphic matroid parity problem
Pfaffian Pairs and Parities: Counting on Linear Matroid Intersection and Parity Problems
Parity Systems and the Delta-Matroid Intersection Problem
📚 Books worth reading
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🔗 Related topics
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