# 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

Support

## 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 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.