scholarly journals Algebraic Algorithms for Linear Matroid Parity Problems

2014 ◽  
Vol 10 (3) ◽  
pp. 1-26 ◽  
Author(s):  
Ho Yee Cheung ◽  
Lap Chi Lau ◽  
Kai Man Leung
Keyword(s):  
Algebraic Algorithms ◽  
Matroid Parity

Algebraic algorithms for the reliability analysis of multi-state k -out-of- n systems

2019 ◽  
Vol 53 (3) ◽  
pp. 146-149
Author(s):  
Patricia Pascual-Ortigosa ◽  
Eduardo Sáenz-de-Cabezón ◽  
Henry P. Wynn
Keyword(s):  
Reliability Analysis ◽  
Algebraic Algorithms

Parallel algorithms for matroid intersection and matroid parity

2015 ◽  
Vol 07 (02) ◽  
pp. 1550019
Author(s):  
Jinyu Huang
Keyword(s):  
Parallel Algorithms ◽  
Polynomial Identity ◽  
Black Box ◽  
Matroid Intersection ◽  
Polynomial Identity Testing ◽  
Identity Testing ◽  
Common Base ◽  
Graphic Matroid ◽  
Matroid Parity ◽  
Nc Algorithms

A maximum linear matroid parity set is called a basic matroid parity set, if its size is the rank of the matroid. We show that determining the existence of a common base (basic matroid parity set) for linear matroid intersection (linear matroid parity) is in NC2, provided that there are polynomial number of common bases (basic matroid parity sets). For graphic matroids, we show that finding a common base for matroid intersection is in NC2, if the number of common bases is polynomial bounded. To our knowledge, these algorithms are the first deterministic NC algorithms for matroid intersection and matroid parity. We also give a new RNC2 algorithm that finds a common base for graphic matroid intersection. We prove that if there is a black-box NC algorithm for Polynomial Identity Testing (PIT), then there is an NC algorithm to determine the existence of a common base (basic matroid parity set) for linear matroid intersection (linear matroid parity).

An augmenting path algorithm for linear matroid parity

COMBINATORICA ◽  
1986 ◽  
Vol 6 (2) ◽  
pp. 123-150 ◽  
Author(s):  
Harold N. Gabow ◽  
Matthias Stallmann
Keyword(s):  
Augmenting Path ◽  
Matroid Parity

scholarly journals Algebraic Algorithms for Even Circuits in Graphs

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 859
Author(s):  
Huy Tài Hà ◽  
Susan Morey
Keyword(s):  
Algebraic Algorithms ◽  
Directed Cycles

We present an algebraic algorithm to detect the existence of and to list all indecomposable even circuits in a given graph. We also discuss an application of our work to the study of directed cycles in digraphs.

scholarly journals On matroid parity and matching polytopes

2020 ◽  
Vol 284 ◽  
pp. 322-331
Author(s):  
Konstantinos Kaparis ◽  
Adam N. Letchford ◽  
Ioannis Mourtos
Keyword(s):  
Matching Polytopes ◽  
Matroid Parity
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