pgr_dijkstraCost¶
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.
Availability
Version 3.1.0
New Proposed functions:
pgr_dijkstraCost(combinations)
Version 2.2.0
New Official function
Description¶
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.
 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: \(O( start\_vids  * (V \log V + E))\)
Signatures¶
Summary
pgr_dijkstraCost(edges_sql, from_vid, to_vid [, directed])
pgr_dijkstraCost(edges_sql, from_vid, to_vids [, directed])
pgr_dijkstraCost(edges_sql, from_vids, to_vid [, directed])
pgr_dijkstraCost(edges_sql, from_vids, to_vids [, directed])
pgr_dijkstraCost(edges_sql, combinations_sql [, directed])  Proposed on v3.1
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET
Using defaults
pgr_dijkstraCost(edges_sql, from_vid, to_vid)
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET
 Example
From vertex \(2\) to vertex \(3\) on a directed graph
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)
One to One¶
pgr_dijkstraCost(edges_sql, from_vid, to_vid [, directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET
 Example
From vertex \(2\) to vertex \(3\) on an undirected graph
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)
One to Many¶
pgr_dijkstraCost(edges_sql, from_vid, to_vids [, directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET
 Example
From vertex \(2\) to vertices \(\{3, 11\}\) on a directed graph
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)
Many to One¶
pgr_dijkstraCost(edges_sql, from_vids, to_vid [, directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET
 Example
From vertices \(\{2, 7\}\) to vertex \(3\) on a directed graph
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)
Many to Many¶
pgr_dijkstraCost(edges_sql, from_vids, to_vids [, directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET
 Example
From vertices \(\{2, 7\}\) to vertices \(\{3, 11\}\) on a directed graph
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)
Combinations¶
pgr_dijkstraCost(TEXT edges_sql, TEXT combination_sql, BOOLEAN directed:=true);
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET
 Example
Using a combinations table on an undirected graph
SELECT * FROM pgr_dijkstraCost(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
'SELECT source, target FROM combinations_table',
FALSE
);
start_vid  end_vid  agg_cost
++
1  2  1
1  4  3
2  1  1
2  4  2
(4 rows)
Parameters¶
Parameter 
Type 
Default 
Description 

Edges SQL 

Edges query as described below 

Combinations SQL 

Combinations query as described below 

start_vid 

Identifier of the starting vertex of the path. 

start_vids 

Array of identifiers of starting vertices. 

end_vid 

Identifier of the ending vertex of the path. 

end_vids 

Array of identifiers of ending vertices. 

directed 



Inner query¶
Edges query¶
Column 
Type 
Default 
Description 

id 

Identifier of the edge. 

source 

Identifier of the first end point vertex of the edge. 

target 

Identifier of the second end point vertex of the edge. 

cost 

Weight of the edge (source, target)


reverse_cost 

1 
Weight of the edge (target, source),

Where:
 ANYINTEGER
SMALLINT, INTEGER, BIGINT
 ANYNUMERICAL
SMALLINT, INTEGER, BIGINT, REAL, FLOAT
Combinations query¶
Column 
Type 
Default 
Description 

source 

Identifier of the first end point vertex of the edge. 

target 

Identifier of the second end point vertex of the edge. 
Where:
 ANYINTEGER
SMALLINT, INTEGER, BIGINT
Return Columns¶
Returns SET OF (start_vid, end_vid, agg_cost)
Column 
Type 
Description 

start_vid 

Identifier of the starting vertex. 
end_vid 

Identifier of the ending vertex. 
agg_cost 

Aggregate cost from 
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)
 Example 3
Four manually assigned (source, target) vertex combinations
SELECT * FROM pgr_dijkstraCost(
'SELECT id, source, target, cost FROM edge_table',
'SELECT * FROM (VALUES (2, 3), (2, 5), (11, 3), (11, 5)) AS combinations (source, target)',
FALSE
);
start_vid  end_vid  agg_cost
++
2  3  3
2  5  1
11  3  2
11  5  2
(4 rows)
See Also¶
Indices and tables