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

A Parallel Shortest Augmenting Path Algorithm for the Assignment Problem

1989 ◽  
Author(s):  
Egon Balas ◽  
Donald Miller ◽  
Joseph Pekny ◽  
Paolo Toth
Keyword(s):  
Assignment Problem ◽  
Augmenting Path

Computer algorithms

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Data Structures ◽  
Analysis Of Algorithms ◽  
Shortest Paths ◽  
Minimum Cut ◽  
Network Data ◽  
Computer Algorithms ◽  
Breadth First Search ◽  
Augmenting Path ◽  
Basic Concepts ◽  
Maximum Flows

This chapter introduces some of the fundamental concepts of numerical network calculations. The chapter starts with a discussion of basic concepts of computational complexity and data structures for storing network data, then progresses to the description and analysis of algorithms for a range of network calculations: breadth-first search and its use for calculating shortest paths, shortest distances, components, closeness, and betweenness; Dijkstra's algorithm for shortest paths and distances on weighted networks; and the augmenting path algorithm for calculating maximum flows, minimum cut sets, and independent paths in networks.

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).

Online Max-flow Learning via Augmenting and De-augmenting Path

2018 ◽  
Author(s):  
Shaoning Pang ◽  
Lei Zhu ◽  
Tao Bany ◽  
Kazushi Ikeda ◽  
Wangfei Zhang ◽  
...  
Keyword(s):  
Augmenting Path

An augmenting path method for solving Linear Bottleneck Assignment problems

Computing ◽  
1978 ◽  
Vol 19 (4) ◽  
pp. 285-295 ◽  
Author(s):  
U. Derigs ◽  
U. Zimmermann
Keyword(s):  
Assignment Problems ◽  
Augmenting Path

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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