pgr_johnson¶
Synopsis¶
pgr_johnson  Returns the sum of the costs of the shortest path for each pair of nodes in the graph using FloydWarshall algorithm.
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,
Characteristics¶
 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.
Signature Summary¶
pgr_johnson(edges_sql)
pgr johnson(edges_sql, directed)
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET
Signatures¶
Minimal Signature¶
pgr_johnson(edges_sql)
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET
Example 1:  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:  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)
Description of the Signatures¶
Description of the edges_sql query¶
edges_sql:  an SQL query, which should return a set of rows with the following columns: 

Column  Type  Default  Description 

source  ANYINTEGER  Identifier of the first end point vertex of the edge.  
target  ANYINTEGER  Identifier of the second end point vertex of the edge.  
cost  ANYNUMERICAL 


reverse_cost  ANYNUMERICAL  1 

Where:
ANYINTEGER:  SMALLINT, INTEGER, BIGINT 

ANYNUMERICAL:  SMALLINT, INTEGER, BIGINT, REAL, FLOAT 
Description of the parameters of the signatures¶
Receives (edges_sql, directed)
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 
Description of the return values¶
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. 
History
 Redesign of pgr_apspJohnson in Version 2.2.0
See Also¶
 pgr_floydWarshall
 Boost Johnson algorithm implementation.
 Queries uses the Sample Data network.
Indices and tables