pgr_johnson  pgRouting Manual (3.4)
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

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
 Example :

For a directed subgraph with edges \(\{1, 2, 3, 4\}\) .
SELECT * FROM pgr_johnson(
'SELECT source, target, 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 7 1
(3 rows)
Parameters
Parameter 
Type 
Default 
Description 


Edges SQL as described below. 
Optional parameters
Column 
Type 
Default 
Description 





Inner Queries
Edges SQL
Column 
Type 
Default 
Description 


ANYINTEGER 
Identifier of the first end point vertex of the edge. 


ANYINTEGER 
Identifier of the second end point vertex of the edge. 


ANYNUMERICAL 
Weight of the edge (



ANYNUMERICAL 
1 
Weight of the edge (

Where:
 ANYINTEGER :

SMALLINT
,INTEGER
,BIGINT
 ANYNUMERICAL :

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



Identifier of the starting vertex. 


Identifier of the ending vertex. 


Aggregate cost from

See Also

Boost Johnson

Queries uses the Sample Data network.
Indices and tables