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.

_images/boost-inside.jpeg — Boost Graph Inside¶

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

Using defaults

pgr_floydWarshall(edges_sql)
RETURNS SET OF (start_vid, end_vid,  agg_cost)
OR EMPTY SET

Example 1: For vertices \(\{1, 2, 3, 4\}\) on a directed graph

SELECT * FROM pgr_floydWarshall(
    'SELECT id, source, target, cost FROM edge_table where id < 5'
);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         1 |       2 |        1
         1 |       5 |        2
         2 |       5 |        1
(3 rows)

Complete Signature¶

pgr_floydWarshall(edges_sql [, directed])
RETURNS SET OF (start_vid, end_vid,  agg_cost)
OR EMPTY SET

Example 2: For vertices \(\{1, 2, 3, 4\}\) on an undirected graph

SELECT * FROM pgr_floydWarshall(
    'SELECT id, source, target, cost FROM edge_table where id < 5',
    false
);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         1 |       2 |        1
         1 |       5 |        2
         2 |       1 |        1
         2 |       5 |        1
         5 |       1 |        2
         5 |       2 |        1
(6 rows)

Parameters¶

Parameter	Type	Description
edges_sql	`TEXT`	SQL query as described above.
directed	`BOOLEAN`	(optional) Default is true (is directed). When set to false the graph is considered as Undirected

Inner query¶

Description of the edges_sql query (id is not necessary)

edges_sql: an SQL query, which should return a set of rows with the following columns:

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) When negative: edge (source, target) does not exist, therefore it’s not part of the graph.
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 (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`	Total cost from `start_vid` to `end_vid`.