Supported versions: Latest (3.3) 3.2 3.1 3.0
Unsupported versions: 2.6 2.5 2.4 2.3 2.2 2.1 2.0

`pgr_johnson`¶

pgr_johnson - 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 Johnson 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 sparse graphs. It usees the Boost’s implementation which runs in \(O(V E \log V)\) 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 johnson(Edges SQL [, directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

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

SELECT * FROM pgr_johnson(
    'SELECT source, target, cost FROM edge_table WHERE id < 5
         ORDER BY id',
    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	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 query¶

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¶

Returns set of (start_vid, end_vid, agg_cost)

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`.

pgr_johnson¶