# 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.

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.

## Signatures¶

Summary

pgr_johnson(edges_sql)
pgr johnson(edges_sql [, directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET


Using default

pgr_johnson(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_johnson(
'SELECT source, target, cost FROM edge_table WHERE id < 5
ORDER BY id'
);
start_vid | end_vid | agg_cost
-----------+---------+----------
1 |       2 |        1
1 |       5 |        2
2 |       5 |        1
(3 rows)



### Complete Signature¶

pgr_johnson(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_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

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.