pgr_aStarCost¶
pgr_aStarCost
- Total cost of the shortest path(s) using the A* algorithm.
Availability
- Version 3.2.0
- New proposed signature:
pgr_aStarCost
(Combinations)
- New proposed signature:
- 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(s)
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
- first by
- 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 \(0\)
- If there is no path from \(v\) to \(u\):
- 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
pgr_aStarCost(Edges SQL, start vid, end vid [, directed] [, heuristic] [, factor] [, epsilon]) pgr_aStarCost(Edges SQL, start vid, end vids [, directed] [, heuristic] [, factor] [, epsilon]) pgr_aStarCost(Edges SQL, start vids, end vid [, directed] [, heuristic] [, factor] [, epsilon]) pgr_aStarCost(Edges SQL, start vids, end vids [, directed] [, heuristic] [, factor] [, epsilon]) pgr_aStarCost(Edges SQL, Combinations SQL [, directed] [, heuristic] [, factor] [, epsilon]) RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET
One to One¶
pgr_aStarCost(Edges SQL, start vid, end vid [, directed] [, heuristic] [, factor] [, epsilon]) RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET
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¶
pgr_aStarCost(Edges SQL, start vid, end vids [, directed] [, heuristic] [, factor] [, epsilon]) RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET
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¶
pgr_aStarCost(Edges SQL, start vids, end vid [, directed] [, heuristic] [, factor] [, epsilon]) RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET
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¶
pgr_aStarCost(Edges SQL, start vids, end vids [, directed] [, heuristic] [, factor] [, epsilon]) RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET
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¶
pgr_aStarCost(Edges SQL, Combinations SQL [, directed] [, heuristic] [, factor] [, epsilon]) RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET
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 | TEXT |
Edges SQL as described below |
Combinations SQL | TEXT |
Combinations SQL 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. |
Optional parameters¶
Column | Type | Default | Description |
---|---|---|---|
directed |
BOOLEAN |
true |
|
aStar optional Parameters¶
Parameter | Type | Default | Description |
---|---|---|---|
heuristic |
INTEGER |
5 | Heuristic number. Current valid values 0~5.
|
factor |
FLOAT |
1 |
For units manipulation. \(factor > 0\). |
epsilon |
FLOAT |
1 |
For less restricted results. \(epsilon >= 1\). |
See heuristics available and factor handling.
Inner Queries¶
Edges SQL¶
Parameter | 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 (
|
|
reverse_cost |
ANY-NUMERICAL | -1 | Weight of the edge (
|
x1 |
ANY-NUMERICAL | X coordinate of source vertex. |
|
y1 |
ANY-NUMERICAL | Y coordinate of source vertex. |
|
x2 |
ANY-NUMERICAL | X coordinate of target vertex. |
|
y2 |
ANY-NUMERICAL | Y coordinate of target vertex. |
Where:
ANY-INTEGER: | SMALLINT , INTEGER , BIGINT |
---|---|
ANY-NUMERICAL: | SMALLINT , INTEGER , BIGINT , REAL , FLOAT |
Combinations SQL¶
Parameter | Type | Description |
---|---|---|
source |
ANY-INTEGER | Identifier of the departure vertex. |
target |
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 |
---|---|---|
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_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)