https://github.com/ahojukka5/graphordering.jl
GraphOrdering.jl is a package focused on a problem of renumbering vertices of a graph such a way that the bandwidth of the sparse matrix is minimized. In other words: find a permutation of system of equations which minimized the fill-in of sparse matrix during matrix factorization. The functionality of the package corresponds to the symrcm function of MATLAB.
https://github.com/ahojukka5/graphordering.jl
bandwidth cuthill graph matrices mckee minimum ordering reverse sparse
Last synced: about 1 month ago
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GraphOrdering.jl is a package focused on a problem of renumbering vertices of a graph such a way that the bandwidth of the sparse matrix is minimized. In other words: find a permutation of system of equations which minimized the fill-in of sparse matrix during matrix factorization. The functionality of the package corresponds to the symrcm function of MATLAB.
- Host: GitHub
- URL: https://github.com/ahojukka5/graphordering.jl
- Owner: ahojukka5
- License: mit
- Created: 2020-04-11T07:27:14.000Z (about 5 years ago)
- Default Branch: master
- Last Pushed: 2020-04-16T12:41:56.000Z (about 5 years ago)
- Last Synced: 2025-01-22T03:41:38.466Z (3 months ago)
- Topics: bandwidth, cuthill, graph, matrices, mckee, minimum, ordering, reverse, sparse
- Language: Julia
- Homepage: https://ahojukka5.github.io/GraphOrdering.jl/dev
- Size: 406 KB
- Stars: 0
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# GraphOrdering.jl
[![][travis-img]][travis-url]
[![][coveralls-img]][coveralls-url]
Package author: Jukka Aho (@ahojukka5)
GraphOrdering.jl is a package focused on a problem of renumbering vertices of a
graph such a way that the bandwidth of the sparse matrix is minimized. In other
words: find a permutation of system of equations which minimized the fill-in of
sparse matrix during matrix factorization. The functionality of the package
corresponds to the `symrcm` function of MATLAB.
## Usage
Consider the following graph:
5--7--6
| | /
4--8--2
| | |
9--1--3
```julia
G = Dict(
1 => [9, 8, 3],
2 => [6, 7, 8, 3],
3 => [2, 1],
4 => [8, 9],
5 => [7, 8],
6 => [7, 2],
7 => [5, 6, 2],
8 => [1, 2, 4, 5],
9 => [4, 1])
result = symrcm(G, 9)
G2 = reorder(G, result)
bandwidth(G), bandwidth(G2)
# output
(17, 7)
```
That is, bandwidth is reduced from 17 to 7.
[travis-img]: https://travis-ci.org/ahojukka5/GraphOrdering.jl.svg?branch=master
[travis-url]: https://travis-ci.org/ahojukka5/GraphOrdering.jl
[coveralls-img]: https://coveralls.io/repos/github/ahojukka5/GraphOrdering.jl/badge.svg?branch=master
[coveralls-url]: https://coveralls.io/github/ahojukka5/GraphOrdering.jl?branch=master