pgr_johnson
 Returns the sum of the costs of the shortest path for each
pair of nodes in the graph using FloydWarshall algorithm.
Availability
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,
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)
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)
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 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  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 
Weight of the edge (source, target)


reverse_cost  ANYNUMERICAL 
1  Weight of the edge (target, source),

Where:
ANYINTEGER:  SMALLINT, INTEGER, BIGINT 

ANYNUMERICAL:  SMALLINT, INTEGER, BIGINT, REAL, FLOAT 
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 . 
Indices and tables