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
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 as described below. 
Optional parameters¶
Column 
Type 
default 
Description 





Inner query¶
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¶
Returns set of (start_vid, end_vid, agg_cost)
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 algorithm implementation.
Queries uses the Sample Data network.
Indices and tables