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
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 |
TEXT |
|
Edges query as described below |
| Combinations SQL |
TEXT |
|
Combinations query as described below |
| 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 |
- When
true Graph is considered Directed
- When
false the graph is considered as Undirected.
|
Inner query
Edges query
| 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)
- When negative: edge (source, target) does not exist, therefore it’s not part of the graph.
|
| reverse_cost |
ANY-NUMERICAL |
-1 |
Weight of the edge (target, source),
- When negative: edge (target, source) does not exist, therefore it’s not part of the graph.
|
Where:
| ANY-INTEGER: | SMALLINT, INTEGER, BIGINT |
|---|
| ANY-NUMERICAL: | SMALLINT, INTEGER, BIGINT, REAL, FLOAT |
|---|
Combinations query
| Column |
Type |
Default |
Description |
|---|
| 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. |
Where:
| ANY-INTEGER: | SMALLINT, INTEGER, BIGINT |
|---|
Return Columns
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 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)
| 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
