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 non-negative 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 \(\infty\).
- When the starting vertex and ending vertex are the same, there is no path.
- Let be the case the values returned are stored in a table:
- The unique index would be the pair:
(start_vid, end_vid)
.
- The unique index would be the pair:
- 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_dijkstraCost(Edges SQL, start vids [, directed]) RETURNS SET OF (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 | TEXT |
Edges SQL as described below |
start vids | ARRAY[BIGINT] |
Array of identifiers of starting vertices. |
Optional parameters¶
Column | Type | Default | Description |
---|---|---|---|
directed |
BOOLEAN |
true |
|
Inner Queries¶
Edges SQL¶
Column | Type | Default | Description |
---|---|---|---|
id |
ANY-INTEGER | Identifier of the edge. | |
source |
ANY-INTEGER | Identifier of the first end point vertex of the edge. | |
target |
ANY-INTEGER | Identifier of the second end point vertex of the edge. | |
cost |
ANY-NUMERICAL | Weight of the edge (source , target ) |
|
reverse_cost |
ANY-NUMERICAL | -1 | Weight of the edge (
|
Where:
ANY-INTEGER: | SMALLINT , INTEGER , BIGINT |
---|---|
ANY-NUMERICAL: | SMALLINT , INTEGER , BIGINT , REAL , FLOAT |
Result Columns¶
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 from start_vid to end_vid . |
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¶
- Dijkstra - Family of functions
- Cost Matrix - Category
- Traveling Sales Person - Family of functions
- Sample Data
Indices and tables