# pgr_cuthillMckeeOrdering - Experimental¶

pgr_cuthillMckeeOrdering — Returns the reverse Cuthill-Mckee ordering of an undirected graphs

Warning

Possible server crash

• These functions might create a server crash

Warning

Experimental functions

• They are not officially of the current release.

• They likely will not be officially be part of the next release:

• The functions might not make use of ANY-INTEGER and ANY-NUMERICAL

• Name might change.

• Signature might change.

• Functionality might change.

• pgTap tests might be missing.

• Might need c/c++ coding.

• May lack documentation.

• Documentation if any might need to be rewritten.

• Documentation examples might need to be automatically generated.

• Might need a lot of feedback from the comunity.

• Might depend on a proposed function of pgRouting

• Might depend on a deprecated function of pgRouting

Availability

• Version 3.4.0

• New experimental function

## Description¶

In numerical linear algebra, the Cuthill-McKee algorithm (CM), named after Elizabeth Cuthill and James McKee, is an algorithm to permute a sparse matrix that has a symmetric sparsity pattern into a band matrix form with a small bandwidth.

The vertices are basically assigned a breadth-first search order, except that at each step, the adjacent vertices are placed in the queue in order of increasing degree.

The main Characteristics are:

• The implementation is for undirected graphs.

• The bandwidth minimization problems are considered NP-complete problems.

• The running time complexity is: $$O(m log(m)|V|)$$

• where $$|V|$$ is the number of vertices,

• $$m$$ is the maximum degree of the vertices in the graph.

## Signatures¶

pgr_cuthillMckeeOrdering(Edges SQL)
RETURNS SET OF (seq, node)
OR EMPTY SET
Example:

Graph ordering of pgRouting Sample Data

SELECT * FROM pgr_cuthillMckeeOrdering(
'SELECT id, source, target, cost, reverse_cost FROM edges'
);
seq | node
-----+------
1 |   13
2 |   14
3 |    2
4 |    4
5 |    1
6 |    9
7 |    3
8 |    8
9 |    5
10 |    7
11 |   12
12 |    6
13 |   11
14 |   17
15 |   10
16 |   16
17 |   15
(17 rows)



## Parameters¶

Parameter

Type

Description

Edges SQL

TEXT

Edges SQL as described below.

## Inner Queries¶

### Edges SQL¶

Column

Type

Default

Description

id

ANY-INTEGER

Identifier of the edge.

source

ANY-INTEGER

Identifier of the first end point vertex of the edge.

target

ANY-INTEGER

Identifier of the second end point vertex of the edge.

cost

ANY-NUMERICAL

Weight of the edge (source, target)

reverse_cost

ANY-NUMERICAL

-1

Weight of the edge (target, source)

• When negative: edge (target, source) does not exist, therefore it’s not part of the graph.

Where:

ANY-INTEGER:

SMALLINT, INTEGER, BIGINT

ANY-NUMERICAL:

SMALLINT, INTEGER, BIGINT, REAL, FLOAT

## Result Columns¶

Returns SET OF (seq, node)

Column

Type

Description

seq

BIGINT

Sequence of the order starting from 1.

node

BIGINT

New ordering in reverse order.