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.

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

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.

See Also

• pgr_johnson

• Boost floyd-Warshall

• Queries uses the Sample Data network.

Indices and tables

• Index

• Search Page