An augmenting path algorithm for linear matroid parity

Harold N. Gabow; Matthias Stallmann

doi:10.1007/bf02579169

An augmenting path algorithm for linear matroid parity

COMBINATORICA ◽

10.1007/bf02579169 ◽

1986 ◽

Vol 6 (2) ◽

pp. 123-150 ◽

Cited By ~ 32

Author(s):

Harold N. Gabow ◽

Matthias Stallmann

Keyword(s):

Augmenting Path ◽

Matroid Parity

Download Full-text

A Parallel Shortest Augmenting Path Algorithm for the Assignment Problem

10.21236/ada233588 ◽

1989 ◽

Cited By ~ 8

Author(s):

Egon Balas ◽

Donald Miller ◽

Joseph Pekny ◽

Paolo Toth

Keyword(s):

Assignment Problem ◽

Augmenting Path

Download Full-text

Computer algorithms

10.1093/oso/9780198805090.003.0008 ◽

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.

Download Full-text

Parallel algorithms for matroid intersection and matroid parity

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830915500196 ◽

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).

Download Full-text