pgr_dijkstraCostMatrix
¶
pgr_dijkstraCostMatrix
 Calculates a cost matrix using pgr_dijkstra.
Availability
Version 3.0.0
Official function
Version 2.3.0
New proposed function
Description¶
Using Dijkstra algorithm, calculate and return a cost matrix.
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.
The main Characteristics are:
Can be used as input to pgr_TSP.
Use directly when the resulting matrix is symmetric and there is no \(\infty\) value.
It will be the users responsibility to make the matrix symmetric.
By using geometric or harmonic average of the non symmetric values.
By using max or min the non symmetric values.
By setting the upper triangle to be the mirror image of the lower triangle.
By setting the lower triangle to be the mirror image of the upper triangle.
It is also the users responsibility to fix an \(\infty\) value.
Each function works as part of the family it belongs to.
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.
When the starting vertex and ending vertex are the same, there is no path.
The aggregate cost in 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 in the non included values (u, v) is \(\infty\).
Let be the case the values returned are stored in a table:
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 vids are ignored.
The returned values are ordered:
start_vid
ascendingend_vid
ascending
Signatures¶
Summary
pgr_dijkstraCostMatrix(Edges SQL, start vids, [directed
])
(start_vid, end_vid, agg_cost)
 Example:
Symmetric cost matrix for vertices \(\{5, 6, 10, 15\}\) on an undirected graph
SELECT * FROM pgr_dijkstraCostMatrix(
'SELECT id, source, target, cost, reverse_cost FROM edges',
(SELECT array_agg(id)
FROM vertices
WHERE id IN (5, 6, 10, 15)),
false);
start_vid  end_vid  agg_cost
++
5  6  1
5  10  2
5  15  3
6  5  1
6  10  1
6  15  2
10  5  2
10  6  1
10  15  1
15  5  3
15  6  2
15  10  1
(12 rows)
Parameters¶
Column 
Type 
Description 


Edges SQL as described below 

start vids 

Array of identifiers of starting 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
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:
Use with pgr_TSP.
SELECT * FROM pgr_TSP(
$$
SELECT * FROM pgr_dijkstraCostMatrix(
'SELECT id, source, target, cost, reverse_cost FROM edges',
(SELECT array_agg(id)
FROM vertices
WHERE id IN (5, 6, 10, 15)),
false)
$$);
NOTICE: pgr_TSP no longer solving with simulated annaeling
HINT: Ignoring annaeling parameters
seq  node  cost  agg_cost
+++
1  5  0  0
2  6  1  1
3  10  1  2
4  15  1  3
5  5  3  6
(5 rows)
See Also¶
Indices and tables