pgr_dijkstraCost¶
Synopsis¶
pgr_dijkstraCost
Using Dijkstra algorithm implemented by Boost.Graph, and extract only the aggregate cost of the shortest path(s) found, for the combination of vertices given.
The pgr_dijkstraCost algorithm, is a good choice to calculate the sum of the costs of the shortest path for a subset of pairs of nodes of the graph. We make use of the Boost’s implementation of dijkstra which runs in \(O(V \log V + E)\) time.
Characteristics¶
 The main Characteristics are:
 It does not return a path.
 Returns the sum of the costs of the shortest path for pair combination of nodes in the graph.
 Process is done only on edges with positive costs.
 Values are returned when there is a path.
 The returned values are in the form of a set of (start_vid, end_vid, agg_cost).
 When the starting vertex and ending vertex are the same, there is no path.
 The agg_cost int the non included values (v, v) is 0
 When the starting vertex and ending vertex are the different and there is no path.
 The agg_cost in the non included values (u, v) is \(\infty\)
 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 undirected graphs, the results are symmetric.
 The agg_cost of (u, v) is the same as for (v, u).
 Any duplicated value in the start_vids or end_vids is ignored.
 The returned values are ordered:
 start_vid ascending
 end_vid ascending
 Running time: \(O( start\_vids  * (V \log V + E))\)
Signature Summary¶
pgr_dijkstraCost(edges_sql, start_vid, end_vid);
pgr_dijkstraCost(edges_sql, start_vid, end_vid, directed);
pgr_dijkstraCost(edges_sql, start_vids, end_vid, directed);
pgr_dijkstraCost(edges_sql, start_vid, end_vids, directed);
pgr_dijkstraCost(edges_sql, start_vids, end_vids, directed);
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET
Signatures¶
Minimal signature¶
The minimal signature is for a directed graph from one start_vid to one end_vid:
pgr_dijkstraCost(TEXT edges_sql, BIGINT start_vid, BIGINT end_vid)
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET
Example
SELECT * FROM pgr_dijkstraCost(
'select id, source, target, cost, reverse_cost from edge_table',
2, 3);
start_vid  end_vid  agg_cost
++
2  3  5
(1 row)
pgr_dijkstraCost One to One¶
 This signature performs a Dijkstra from one start_vid to one end_vid:
 on a directed graph when directed flag is missing or is set to true.
 on an undirected graph when directed flag is set to false.
pgr_dijkstraCost(TEXT edges_sql, BIGINT start_vid, BIGINT end_vid,
BOOLEAN directed:=true);
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET
Example: 

SELECT * FROM pgr_dijkstraCost(
'select id, source, target, cost, reverse_cost from edge_table',
2, 3, false);
start_vid  end_vid  agg_cost
++
2  3  1
(1 row)
pgr_dijkstraCost One to Many¶
pgr_dijkstraCost(TEXT edges_sql, BIGINT start_vid, array[ANY_INTEGER] end_vids,
BOOLEAN directed:=true);
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET
 This signature performs a Dijkstra from one start_vid to each end_vid in end_vids:
 on a directed graph when directed flag is missing or is set to true.
 on an undirected graph when directed flag is set to false.
Example: 

SELECT * FROM pgr_dijkstraCost(
'select id, source, target, cost, reverse_cost from edge_table',
2, ARRAY[3, 11]);
start_vid  end_vid  agg_cost
++
2  3  5
2  11  3
(2 rows)
pgr_dijkstraCost Many to One¶
pgr_dijkstraCost(TEXT edges_sql, array[ANY_INTEGER] start_vids, BIGINT end_vid,
BOOLEAN directed:=true);
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET
 This signature performs a Dijkstra from each start_vid in start_vids to one end_vid:
 on a directed graph when directed flag is missing or is set to true.
 on an undirected graph when directed flag is set to false.
Example: 

SELECT * FROM pgr_dijkstraCost(
'select id, source, target, cost, reverse_cost from edge_table',
ARRAY[2, 7], 3);
start_vid  end_vid  agg_cost
++
2  3  5
7  3  6
(2 rows)
pgr_dijkstraCost Many to Many¶
pgr_dijkstraCost(TEXT edges_sql, array[ANY_INTEGER] start_vids, array[ANY_INTEGER] end_vids,
BOOLEAN directed:=true);
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET
 This signature performs a Dijkstra from each start_vid in start_vids to each end_vid in end_vids:
 on a directed graph when directed flag is missing or is set to true.
 on an undirected graph when directed flag is set to false.
Example: 

SELECT * FROM pgr_dijkstraCost(
'select id, source, target, cost, reverse_cost from edge_table',
ARRAY[2, 7], ARRAY[3, 11]);
start_vid  end_vid  agg_cost
++
2  3  5
2  11  3
7  3  6
7  11  4
(4 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 

id  ANYINTEGER  Identifier of the edge.  
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¶
Column  Type  Default  Description 

sql  TEXT  SQL query as described above.  
start_vid  BIGINT  Identifier of the starting vertex of the path.  
start_vids  ARRAY[BIGINT]  Array of identifiers of starting vertices.  
end_vid  BIGINT  Identifier of the ending vertex of the path.  
end_vids  ARRAY[BIGINT]  Array of identifiers of ending vertices.  
directed  BOOLEAN  true 

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  Aggregate cost of the shortest path from start_vid to end_vid. 
Additional Examples¶
Example 1:  Demonstration of repeated values are ignored, and result is sorted. 

SELECT * FROM pgr_dijkstraCost(
'select id, source, target, cost, reverse_cost from edge_table',
ARRAY[5, 3, 4, 3, 3, 4], ARRAY[3, 5, 3, 4]);
start_vid  end_vid  agg_cost
++
3  4  3
3  5  2
4  3  1
4  5  3
5  3  4
5  4  3
(6 rows)
Example 2:  Making start_vids the same as end_vids 

SELECT * FROM pgr_dijkstraCost(
'select id, source, target, cost, reverse_cost from edge_table',
ARRAY[5, 3, 4], ARRAY[5, 3, 4]);
start_vid  end_vid  agg_cost
++
3  4  3
3  5  2
4  3  1
4  5  3
5  3  4
5  4  3
(6 rows)
History
 New in version 2.2.0
See Also¶
Indices and tables