pgr_johnson  pgRouting Manual (3.0)
pgr_johnson
pgr_johnson
 Returns the sum of the costs of the shortest path for each
pair of nodes in the graph using FloydWarshall 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 

SQL query as described above. 
directed 

(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 

Identifier of the first end point vertex of the edge. 

target 

Identifier of the second end point vertex of the edge. 

cost 

Weight of the edge (source, target)


reverse_cost 

1 
Weight of the edge (target, source) ,

Where:
 ANYINTEGER

SMALLINT, INTEGER, BIGINT
 ANYNUMERICAL

SMALLINT, INTEGER, BIGINT, REAL, FLOAT
Result Columns
Returns set of
(start_vid,
end_vid,
agg_cost)
Column 
Type 
Description 

start_vid 

Identifier of the starting vertex. 
end_vid 

Identifier of the ending vertex. 
agg_cost 

Total cost from

See Also

Boost Johnson algorithm implementation.

Queries uses the Sample Data network.
Indices and tables