pgr_aStarCost¶
pgr_aStarCost
- Total cost of the shortest path using the A* algorithm.
Availability
Version 3.2.0
New proposed signature:
pgr_aStarCost
(Combinations)
Version 3.0.0
Official function
Version 2.4.0
New proposed function
Description¶
The pgr_aStarCost
function sumarizes of the cost of the shortest path
using the A* algorithm.
The main characteristics are:
Process works for directed and undirected graphs.
Ordering is:
first by
start_vid
(if exists)then by
end_vid
Values are returned when there is a path.
Let \(v\) and \(u\) be nodes on the graph:
If there is no path from \(v\) to \(u\):
no corresponding row is returned
agg_cost
from \(v\) to \(u\) is \(\infty\)
There is no path when \(v = u\) therefore
no corresponding row is returned
agg_cost
from v to u is \(0\)
When \((x,y)\) coordinates for the same vertex identifier differ:
A random selection of the vertex’s \((x,y)\) coordinates is used.
Running time: \(O((E + V) * \log V)\)
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)
For undirected graphs, the results are symmetric.
The agg_cost of (u, v) is the same as for (v, u).
The returned values are ordered in ascending order:
start_vid ascending
end_vid ascending
Signatures¶
Summary
[directed, heuristic, factor, epsilon]
(start_vid, end_vid, agg_cost)
One to One¶
[directed, heuristic, factor, epsilon]
(start_vid, end_vid, agg_cost)
- Example:
From vertex \(6\) to vertex \(12\) on a directed graph with heuristic \(2\)
SELECT * FROM pgr_aStarCost(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edges',
6, 12,
directed => true, heuristic => 2);
start_vid | end_vid | agg_cost
-----------+---------+----------
6 | 12 | 3
(1 row)
One to Many¶
[directed, heuristic, factor, epsilon]
(start_vid, end_vid, agg_cost)
- Example:
From vertex \(6\) to vertices \(\{10, 12\}\) on a directed graph with heuristic \(3\) and factor \(3.5\)
SELECT * FROM pgr_aStarCost(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edges',
6, ARRAY[10, 12],
heuristic => 3, factor => 3.5);
start_vid | end_vid | agg_cost
-----------+---------+----------
6 | 10 | 5
6 | 12 | 3
(2 rows)
Many to One¶
[directed, heuristic, factor, epsilon]
(start_vid, end_vid, agg_cost)
- Example:
From vertices \(\{6, 8\}\) to vertex \(10\) on an undirected graph with heuristic \(4\)
SELECT * FROM pgr_aStarCost(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edges',
ARRAY[6, 8], 10,
false, heuristic => 4);
start_vid | end_vid | agg_cost
-----------+---------+----------
6 | 10 | 1
8 | 10 | 3
(2 rows)
Many to Many¶
[directed, heuristic, factor, epsilon]
(start_vid, end_vid, agg_cost)
- Example:
From vertices \(\{6, 8\}\) to vertices \(\{10, 12\}\) on a directed graph with factor \(0.5\)
SELECT * FROM pgr_aStarCost(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edges',
ARRAY[6, 8], ARRAY[10, 12],
factor => 0.5);
start_vid | end_vid | agg_cost
-----------+---------+----------
6 | 10 | 5
6 | 12 | 3
8 | 10 | 5
8 | 12 | 1
(4 rows)
Combinations¶
[directed, heuristic, factor, epsilon]
(start_vid, end_vid, agg_cost)
- Example:
Using a combinations table on a directed graph with factor \(0.5\).
The combinations table:
SELECT * FROM combinations;
source | target
--------+--------
5 | 6
5 | 10
6 | 5
6 | 15
6 | 14
(5 rows)
The query:
SELECT * FROM pgr_aStarCost(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edges',
'SELECT * FROM combinations',
factor => 0.5);
start_vid | end_vid | agg_cost
-----------+---------+----------
5 | 6 | 1
5 | 10 | 6
6 | 5 | 1
6 | 15 | 4
(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 |
---|---|---|---|
|
|
|
|
aStar optional parameters¶
Parameter |
Type |
Default |
Description |
---|---|---|---|
|
|
5 |
Heuristic number. Current valid values 0~5.
|
|
|
|
For units manipulation. \(factor > 0\). |
|
|
|
For less restricted results. \(epsilon >= 1\). |
See heuristics available and factor handling.
Inner Queries¶
Edges SQL¶
Parameter |
Type |
Default |
Description |
---|---|---|---|
|
ANY-INTEGER |
Identifier of the edge. |
|
|
ANY-INTEGER |
Identifier of the first end point vertex of the edge. |
|
|
ANY-INTEGER |
Identifier of the second end point vertex of the edge. |
|
|
ANY-NUMERICAL |
Weight of the edge (
|
|
|
ANY-NUMERICAL |
-1 |
Weight of the edge (
|
|
ANY-NUMERICAL |
X coordinate of |
|
|
ANY-NUMERICAL |
Y coordinate of |
|
|
ANY-NUMERICAL |
X coordinate of |
|
|
ANY-NUMERICAL |
Y coordinate of |
Where:
- ANY-INTEGER:
SMALLINT
,INTEGER
,BIGINT
- ANY-NUMERICAL:
SMALLINT
,INTEGER
,BIGINT
,REAL
,FLOAT
Combinations SQL¶
Parameter |
Type |
Description |
---|---|---|
|
ANY-INTEGER |
Identifier of the departure vertex. |
|
ANY-INTEGER |
Identifier of the arrival vertex. |
Where:
- ANY-INTEGER:
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_aStarCost(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
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_aStarCost(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
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_aStarCost(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
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