pgr_dijkstraCost¶
Synopsis¶
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.
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.
Characteristics¶
- 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: \(O(| start\_vids | * (V \log V + E))\)
Signature Summary¶
pgr_dijkstraCost(edges_sql, start_vid, end_vid);
pgr_dijkstraCost(edges_sql, start_vid, end_vid, directed);
pgr_dijkstraCost(edges_sql, start_vids, end_vid, directed);
pgr_dijkstraCost(edges_sql, start_vid, end_vids, directed);
pgr_dijkstraCost(edges_sql, start_vids, end_vids, directed);
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET
Signatures¶
Minimal signature¶
The minimal signature is for a directed graph from one start_vid to one end_vid:
pgr_dijkstraCost(TEXT edges_sql, BIGINT start_vid, BIGINT end_vid)
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET
Example
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)
pgr_dijkstraCost One to One¶
- This signature performs a Dijkstra from one start_vid to one end_vid:
- on a directed graph when directed flag is missing or is set to true.
- on an undirected graph when directed flag is set to false.
pgr_dijkstraCost(TEXT edges_sql, BIGINT start_vid, BIGINT end_vid,
BOOLEAN directed:=true);
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET
Example: |
---|
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)
pgr_dijkstraCost One to Many¶
pgr_dijkstraCost(TEXT edges_sql, BIGINT start_vid, array[ANY_INTEGER] end_vids,
BOOLEAN directed:=true);
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET
- This signature performs a Dijkstra from one start_vid to each end_vid in end_vids:
- on a directed graph when directed flag is missing or is set to true.
- on an undirected graph when directed flag is set to false.
Example: |
---|
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)
pgr_dijkstraCost Many to One¶
pgr_dijkstraCost(TEXT edges_sql, array[ANY_INTEGER] start_vids, BIGINT end_vid,
BOOLEAN directed:=true);
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET
- This signature performs a Dijkstra from each start_vid in start_vids to one end_vid:
- on a directed graph when directed flag is missing or is set to true.
- on an undirected graph when directed flag is set to false.
Example: |
---|
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)
pgr_dijkstraCost Many to Many¶
pgr_dijkstraCost(TEXT edges_sql, array[ANY_INTEGER] start_vids, array[ANY_INTEGER] end_vids,
BOOLEAN directed:=true);
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET
- This signature performs a Dijkstra from each start_vid in start_vids to each end_vid in end_vids:
- on a directed graph when directed flag is missing or is set to true.
- on an undirected graph when directed flag is set to false.
Example: |
---|
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)
Description of the Signatures¶
Description of the edges_sql query¶
edges_sql: | an SQL query, which should return a set of rows with the following columns: |
---|
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 |
|
|
reverse_cost | ANY-NUMERICAL | -1 |
|
Where:
ANY-INTEGER: | SMALLINT, INTEGER, BIGINT |
---|---|
ANY-NUMERICAL: | SMALLINT, INTEGER, BIGINT, REAL, FLOAT |
Description of the parameters of the signatures¶
Column | Type | Default | Description |
---|---|---|---|
sql | TEXT | SQL query as described above. | |
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 |
|
Description of the return values¶
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 of the shortest path 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)
History
- New in version 2.2.0
See Also¶
Indices and tables