pgr_dijkstraCost
¶
pgr_dijkstraCost
 Total cost of the shortest path(s) using Dijkstra
algorithm.
Availability
Version 3.1.0
New proposed signature:
pgr_dijkstraCost
(Combinations)
Version 2.2.0
New Official function
Description¶
The pgr_dijkstraCost
function sumarizes of the cost of the shortest path(s)
using Dijkstra Algorithm.
Dijkstra’s algorithm, conceived by Dutch computer scientist Edsger Dijkstra in 1956. It is a graph search algorithm that solves the shortest path problem for a graph with nonnegative edge path costs, producing a shortest path from a starting vertex to an ending vertex. This implementation can be used with a directed graph and an undirected graph.
Process is done only on edges with positive costs.
A negative value on a cost column is interpreted as the edge does not exist.
Values are returned when there is a path.
When there is no path:
When the starting vertex and ending vertex are the same.
The aggregate cost of the non included values \((v, v)\) is \(0\)
When the starting vertex and ending vertex are the different and there is no path:
The aggregate cost the non included values \((u, v)\) is \(\infty\)
For optimization purposes, any duplicated value in the starting vertices or on the ending vertices are ignored.
Running time: \(O( start\ vids  * (V \log V + E))\)
It does not return a path.
Returns the sum of the costs of the shortest path of each pair combination of nodes requested.
Let be the case the values returned are stored in a table, so the unique index would be the pair:
(start_vid, end_vid)
.Depending on the function and its parameters, the results can be symmetric.
The aggregate cost of \((u, v)\) is the same as for \((v, u)\).
Any duplicated value in the start or end vertex identifiers are ignored.
The returned values are ordered:
start_vid
ascendingend_vid
ascending
Signatures¶
Summary
pgr_dijkstraCost(Edges SQL, start vid, end vid [, directed]) pgr_dijkstraCost(Edges SQL, start vid, end vids [, directed]) pgr_dijkstraCost(Edges SQL, start vids, end vid [, directed]) pgr_dijkstraCost(Edges SQL, start vids, end vids [, directed]) pgr_dijkstraCost(Edges SQL, Combinations SQL [, directed]) RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET
One to One¶
pgr_dijkstraCost(Edges SQL, start vid, end vid [, directed]) RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET
 Example:
From vertex \(6\) to vertex \(10\) on a directed graph
SELECT * FROM pgr_dijkstraCost(
'SELECT id, source, target, cost, reverse_cost FROM edges',
6, 10, true);
start_vid  end_vid  agg_cost
++
6  10  5
(1 row)
One to Many¶
pgr_dijkstraCost(Edges SQL, start vid, end vids [, directed]) RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET
 Example:
From vertex \(6\) to vertices \(\{10, 17\}\) on a directed graph
SELECT * FROM pgr_dijkstraCost(
'SELECT id, source, target, cost, reverse_cost FROM edges',
6, ARRAY[10, 17]);
start_vid  end_vid  agg_cost
++
6  10  5
6  17  4
(2 rows)
Many to One¶
pgr_dijkstraCost(Edges SQL, start vids, end vid [, directed]) RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET
 Example:
From vertices \(\{6, 1\}\) to vertex \(17\) on a directed graph
SELECT * FROM pgr_dijkstraCost(
'SELECT id, source, target, cost, reverse_cost FROM edges',
ARRAY[6, 1], 17);
start_vid  end_vid  agg_cost
++
1  17  5
6  17  4
(2 rows)
Many to Many¶
pgr_dijkstraCost(Edges SQL, start vids, end vids [, directed]) RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET
 Example:
From vertices \(\{6, 1\}\) to vertices \(\{10, 17\}\) on an undirected graph
SELECT * FROM pgr_dijkstraCost(
'SELECT id, source, target, cost, reverse_cost FROM edges',
ARRAY[6, 1], ARRAY[10, 17],
directed => false);
start_vid  end_vid  agg_cost
++
1  10  4
1  17  5
6  10  1
6  17  4
(4 rows)
Combinations¶
pgr_dijkstraCost(Edges SQL, Combinations SQL [, directed]) RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET
 Example:
Using a combinations table on an undirected graph
The combinations table:
SELECT source, target FROM combinations;
source  target
+
5  6
5  10
6  5
6  15
6  14
(5 rows)
The query:
SELECT * FROM pgr_dijkstraCost(
'SELECT id, source, target, cost, reverse_cost FROM edges',
'SELECT source, target FROM combinations',
false);
start_vid  end_vid  agg_cost
++
5  6  1
5  10  2
6  5  1
6  15  2
(4 rows)
Parameters¶
Column 
Type 
Description 


Edges SQL as described below 


Combinations SQL 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. 
Optional parameters¶
Column 
Type 
Default 
Description 





Inner Queries¶
Edges SQL¶
Column 
Type 
Default 
Description 


ANYINTEGER 
Identifier of the edge. 


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
Combinations SQL¶
Parameter 
Type 
Description 


ANYINTEGER 
Identifier of the departure vertex. 

ANYINTEGER 
Identifier of the arrival vertex. 
Where:
 ANYINTEGER:
SMALLINT
,INTEGER
,BIGINT
Result Columns¶
Set of (start_vid, end_vid, agg_cost)
Column 
Type 
Description 



Identifier of the starting vertex. 


Identifier of the ending vertex. 


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 edges',
ARRAY[7, 10, 15, 10, 10, 15], ARRAY[10, 7, 10, 15]);
start_vid  end_vid  agg_cost
++
7  10  4
7  15  3
10  7  2
10  15  3
15  7  3
15  10  1
(6 rows)
 Example 2:
Making start_vids the same as end_vids
SELECT * FROM pgr_dijkstraCost(
'SELECT id, source, target, cost, reverse_cost FROM edges',
ARRAY[7, 10, 15], ARRAY[7, 10, 15]);
start_vid  end_vid  agg_cost
++
7  10  4
7  15  3
10  7  2
10  15  3
15  7  3
15  10  1
(6 rows)
 Example 3:
Manually assigned vertex combinations.
SELECT * FROM pgr_dijkstraCost(
'SELECT id, source, target, cost, reverse_cost FROM edges',
'SELECT * FROM (VALUES (6, 10), (6, 7), (12, 10)) AS combinations (source, target)');
start_vid  end_vid  agg_cost
++
6  7  1
6  10  5
12  10  4
(3 rows)
See Also¶
Indices and tables