# pgr_floydWarshall¶

pgr_floydWarshall - Returns the sum of the costs of the shortest path for each pair of nodes in the graph using Floyd-Warshall algorithm.

Availability

• Version 2.2.0

• Signature change

• Old signature no longer supported

• Version 2.0.0

• Official function

## Description¶

The Floyd-Warshall algorithm, also known as Floyd’s algorithm, is a good choice to calculate the sum of the costs of the shortest path for each pair of nodes in the graph, for dense graphs. We use Boost’s implementation which runs in $$\Theta(V^3)$$ time,

The main characteristics are:

• It does not return a path.

• Returns the sum of the costs of the shortest path for each pair of nodes in the graph.

• Process is done only on edges with positive costs.

• Boost returns a $$V \times V$$ matrix, where the infinity values. Represent the distance between vertices for which there is no path.

• We return only the non infinity values in form of a set of (start_vid, end_vid, agg_cost).

• Let be the case the values returned are stored in a table, so the unique index would be the pair: (start_vid, end_vid).

• For the undirected graph, the results are symmetric.

• The agg_cost of (u, v) is the same as for (v, u).

• When start_vid = end_vid, the agg_cost = 0.

• Recommended, use a bounding box of no more than 3500 edges.

## Signatures¶

Summary

pgr_floydWarshall(Edges SQL, [directed])

RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET
Example:

For a directed subgraph with edges $$\{1, 2, 3, 4\}$$.

SELECT * FROM pgr_floydWarshall(
'SELECT id, source, target, cost, reverse_cost
FROM edges where id < 5'
) ORDER BY start_vid, end_vid;
start_vid | end_vid | agg_cost
-----------+---------+----------
5 |       6 |        1
5 |       7 |        2
6 |       5 |        1
6 |       7 |        1
7 |       5 |        2
7 |       6 |        1
10 |       5 |        2
10 |       6 |        1
10 |       7 |        2
15 |       5 |        3
15 |       6 |        2
15 |       7 |        3
15 |      10 |        1
(13 rows)



## Parameters¶

Parameter

Type

Default

Description

Edges SQL

TEXT

Edges SQL as described below.

### Optional parameters¶

Column

Type

Default

Description

directed

BOOLEAN

true

• When true the graph is considered Directed

• When false the graph is considered as Undirected.

## Inner Queries¶

### Edges SQL¶

Column

Type

Default

Description

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¶

Set of (start_vid, end_vid, agg_cost)

Column

Type

Description

start_vid

BIGINT

Identifier of the starting vertex.

end_vid

BIGINT

Identifier of the ending vertex.

agg_cost

FLOAT

Aggregate cost from start_vid to end_vid.