pgr_withPoints
- Proposed¶
pgr_withPoints
- Returns the shortest path in a graph with additional
temporary vertices.
Warning
Proposed functions for next mayor release.
They are not officially in the current release.
They will likely officially be part of the next mayor release:
The functions make use of ANY-INTEGER and ANY-NUMERICAL
Name might not change. (But still can)
Signature might not change. (But still can)
Functionality might not change. (But still can)
pgTap tests have being done. But might need more.
Documentation might need refinement.
Availability
Version 3.2.0
New proposed function:
pgr_withPoints(Combinations)
Version 2.2.0
New proposed function
Description¶
Modify the graph to include points defined by points_sql. Using Dijkstra algorithm, find the shortest path(s)
The main characteristics are:
Process is done only on edges with positive costs.
Vertices of the graph are:
positive when it belongs to the edges_sql
negative when it belongs to the points_sql
Values are returned when there is a path.
When the starting vertex and ending vertex are the same, there is no path. - The agg_cost 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 the non included values (u, v) is ∞
For optimization purposes, any duplicated value in the start_vids or end_vids are ignored.
The returned values are ordered: - start_vid ascending - end_vid ascending
Running time: \(O(|start\_vids|\times(V \log V + E))\)
Signatures¶
Summary
[directed, driving_side, details])
(seq, path_seq, [start_pid], [end_pid], node, edge, cost, agg_cost)
One to One¶
(seq, path_seq, node, edge, cost, agg_cost)
- Example:
From point \(1\) to vertex \(10\) with details
SELECT * FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
-1, 10,
details => true);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 | 1 | -1 | 1 | 0.6 | 0
2 | 2 | 6 | 4 | 0.7 | 0.6
3 | 3 | -6 | 4 | 0.3 | 1.3
4 | 4 | 7 | 8 | 1 | 1.6
5 | 5 | 11 | 9 | 1 | 2.6
6 | 6 | 16 | 16 | 1 | 3.6
7 | 7 | 15 | 3 | 1 | 4.6
8 | 8 | 10 | -1 | 0 | 5.6
(8 rows)
One to Many¶
(seq, path_seq, end_pid, node, edge, cost, agg_cost)
- Example:
From point \(1\) to point \(3\) and vertex \(7\) on an undirected graph
SELECT * FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
-1, ARRAY[-3, 7],
directed => false);
seq | path_seq | end_pid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
1 | 1 | -3 | -1 | 1 | 0.6 | 0
2 | 2 | -3 | 6 | 4 | 1 | 0.6
3 | 3 | -3 | 7 | 10 | 1 | 1.6
4 | 4 | -3 | 8 | 12 | 0.6 | 2.6
5 | 5 | -3 | -3 | -1 | 0 | 3.2
6 | 1 | 7 | -1 | 1 | 0.6 | 0
7 | 2 | 7 | 6 | 4 | 1 | 0.6
8 | 3 | 7 | 7 | -1 | 0 | 1.6
(8 rows)
Many to One¶
(seq, path_seq, start_pid, node, edge, cost, agg_cost)
- Example:
From point \(1\) and vertex \(6\) to point \(3\)
SELECT * FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[-1, 6], -3);
seq | path_seq | start_pid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
1 | 1 | -1 | -1 | 1 | 0.6 | 0
2 | 2 | -1 | 6 | 4 | 1 | 0.6
3 | 3 | -1 | 7 | 10 | 1 | 1.6
4 | 4 | -1 | 8 | 12 | 0.6 | 2.6
5 | 5 | -1 | -3 | -1 | 0 | 3.2
6 | 1 | 6 | 6 | 4 | 1 | 0
7 | 2 | 6 | 7 | 10 | 1 | 1
8 | 3 | 6 | 8 | 12 | 0.6 | 2
9 | 4 | 6 | -3 | -1 | 0 | 2.6
(9 rows)
Many to Many¶
(seq, path_seq, start_pid, end_pid, node, edge, cost, agg_cost)
- Example:
From point \(1\) and vertex \(6\) to point \(3\) and vertex \(1\)
SELECT * FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[-1, 6], ARRAY[-3, 1]);
seq | path_seq | start_pid | end_pid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 | 1 | -1 | -3 | -1 | 1 | 0.6 | 0
2 | 2 | -1 | -3 | 6 | 4 | 1 | 0.6
3 | 3 | -1 | -3 | 7 | 10 | 1 | 1.6
4 | 4 | -1 | -3 | 8 | 12 | 0.6 | 2.6
5 | 5 | -1 | -3 | -3 | -1 | 0 | 3.2
6 | 1 | -1 | 1 | -1 | 1 | 0.6 | 0
7 | 2 | -1 | 1 | 6 | 4 | 1 | 0.6
8 | 3 | -1 | 1 | 7 | 7 | 1 | 1.6
9 | 4 | -1 | 1 | 3 | 6 | 1 | 2.6
10 | 5 | -1 | 1 | 1 | -1 | 0 | 3.6
11 | 1 | 6 | -3 | 6 | 4 | 1 | 0
12 | 2 | 6 | -3 | 7 | 10 | 1 | 1
13 | 3 | 6 | -3 | 8 | 12 | 0.6 | 2
14 | 4 | 6 | -3 | -3 | -1 | 0 | 2.6
15 | 1 | 6 | 1 | 6 | 4 | 1 | 0
16 | 2 | 6 | 1 | 7 | 7 | 1 | 1
17 | 3 | 6 | 1 | 3 | 6 | 1 | 2
18 | 4 | 6 | 1 | 1 | -1 | 0 | 3
(18 rows)
Combinations¶
(seq, path_seq, start_pid, end_pid, node, edge, cost, agg_cost)
- Example:
Two combinations
From point \(1\) to vertex \(10\), and from vertex \(6\) to point \(3\) with right side driving.
SELECT * FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
'SELECT * FROM (VALUES (-1, 10), (6, -3)) AS combinations(source, target)',
driving_side => 'r', details => true);
seq | path_seq | start_pid | end_pid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 | 1 | -1 | 10 | -1 | 1 | 0.4 | 0
2 | 2 | -1 | 10 | 5 | 1 | 1 | 0.4
3 | 3 | -1 | 10 | 6 | 4 | 0.7 | 1.4
4 | 4 | -1 | 10 | -6 | 4 | 0.3 | 2.1
5 | 5 | -1 | 10 | 7 | 8 | 1 | 2.4
6 | 6 | -1 | 10 | 11 | 9 | 1 | 3.4
7 | 7 | -1 | 10 | 16 | 16 | 1 | 4.4
8 | 8 | -1 | 10 | 15 | 3 | 1 | 5.4
9 | 9 | -1 | 10 | 10 | -1 | 0 | 6.4
10 | 1 | 6 | -3 | 6 | 4 | 0.7 | 0
11 | 2 | 6 | -3 | -6 | 4 | 0.3 | 0.7
12 | 3 | 6 | -3 | 7 | 10 | 1 | 1
13 | 4 | 6 | -3 | 8 | 12 | 0.6 | 2
14 | 5 | 6 | -3 | -3 | -1 | 0 | 2.6
(14 rows)
Parameters¶
Column |
Type |
Description |
---|---|---|
|
Edges SQL as described below |
|
|
Points SQL as described below |
|
|
Combinations SQL as described below |
|
start vid |
|
Identifier of the starting vertex of the path. Negative value is for point’s identifier. |
start vids |
|
Array of identifiers of starting vertices. Negative values are for point’s identifiers. |
end vid |
|
Identifier of the ending vertex of the path. Negative value is for point’s identifier. |
end vids |
|
Array of identifiers of ending vertices. Negative values are for point’s identifiers. |
Optional parameters¶
Column |
Type |
Default |
Description |
---|---|---|---|
|
|
|
|
With points optional parameters¶
Parameter |
Type |
Default |
Description |
---|---|---|---|
|
|
|
Value in [
|
|
|
|
|
Inner Queries¶
Edges SQL¶
Column |
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 (
|
Where:
- ANY-INTEGER:
SMALLINT
,INTEGER
,BIGINT
- ANY-NUMERICAL:
SMALLINT
,INTEGER
,BIGINT
,REAL
,FLOAT
Points SQL¶
Parameter |
Type |
Default |
Description |
---|---|---|---|
|
ANY-INTEGER |
value |
Identifier of the point.
|
|
ANY-INTEGER |
Identifier of the “closest” edge to the point. |
|
|
ANY-NUMERICAL |
Value in <0,1> that indicates the relative postition from the first end point of the edge. |
|
|
|
|
Value in [
|
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¶
Returns set of (seq, path_seq [, start_pid] [, end_pid], node, edge, cost,
agg_cost)
Column |
Type |
Description |
---|---|---|
|
|
Sequential value starting from 1. |
|
|
Relative position in the path.
|
|
|
Identifier of a starting vertex/point of the path.
|
|
|
Identifier of an ending vertex/point of the path.
|
|
|
Identifier of the node in the path from
|
|
|
Identifier of the edge used to go from
|
|
|
Cost to traverse from
|
|
|
Aggregate cost from
|
Additional Examples¶
Use pgr_findCloseEdges in the Points SQL.¶
Find the routes from vertex \(1\) to the two closest locations on the graph of point (2.9, 1.8).
SELECT * FROM pgr_withPoints(
$e$ SELECT * FROM edges $e$,
$p$ SELECT edge_id, round(fraction::numeric, 2) AS fraction, side
FROM pgr_findCloseEdges(
$$SELECT id, geom FROM edges$$,
(SELECT ST_POINT(2.9, 1.8)),
0.5, cap => 2)
$p$,
1, ARRAY[-1, -2]);
seq | path_seq | end_pid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
1 | 1 | -2 | 1 | 6 | 1 | 0
2 | 2 | -2 | 3 | 7 | 1 | 1
3 | 3 | -2 | 7 | 8 | 0.9 | 2
4 | 4 | -2 | -2 | -1 | 0 | 2.9
5 | 1 | -1 | 1 | 6 | 1 | 0
6 | 2 | -1 | 3 | 7 | 1 | 1
7 | 3 | -1 | 7 | 8 | 1 | 2
8 | 4 | -1 | 11 | 9 | 1 | 3
9 | 5 | -1 | 16 | 16 | 1 | 4
10 | 6 | -1 | 15 | 3 | 1 | 5
11 | 7 | -1 | 10 | 5 | 0.8 | 6
12 | 8 | -1 | -1 | -1 | 0 | 6.8
(12 rows)
Point \(-1\) corresponds to the closest edge from point (2.9, 1.8).
Point \(-2\) corresponds to the next close edge from point (2.9, 1.8).
Usage variations¶
All the examples are about traveling from point \(1\) and vertex \(5\) to points \(\{2, 3, 6\}\) and vertices \(\{10, 11\}\)
SELECT *
FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[5, -1], ARRAY[-2, -3, -6, 10, 11],
driving_side => 'r', details => true);
seq | path_seq | start_pid | end_pid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 | 1 | -1 | -6 | -1 | 1 | 0.4 | 0
2 | 2 | -1 | -6 | 5 | 1 | 1 | 0.4
3 | 3 | -1 | -6 | 6 | 4 | 0.7 | 1.4
4 | 4 | -1 | -6 | -6 | -1 | 0 | 2.1
5 | 1 | -1 | -3 | -1 | 1 | 0.4 | 0
6 | 2 | -1 | -3 | 5 | 1 | 1 | 0.4
7 | 3 | -1 | -3 | 6 | 4 | 0.7 | 1.4
8 | 4 | -1 | -3 | -6 | 4 | 0.3 | 2.1
9 | 5 | -1 | -3 | 7 | 10 | 1 | 2.4
10 | 6 | -1 | -3 | 8 | 12 | 0.6 | 3.4
11 | 7 | -1 | -3 | -3 | -1 | 0 | 4
12 | 1 | -1 | -2 | -1 | 1 | 0.4 | 0
13 | 2 | -1 | -2 | 5 | 1 | 1 | 0.4
14 | 3 | -1 | -2 | 6 | 4 | 0.7 | 1.4
15 | 4 | -1 | -2 | -6 | 4 | 0.3 | 2.1
16 | 5 | -1 | -2 | 7 | 8 | 1 | 2.4
17 | 6 | -1 | -2 | 11 | 9 | 1 | 3.4
18 | 7 | -1 | -2 | 16 | 15 | 0.4 | 4.4
19 | 8 | -1 | -2 | -2 | -1 | 0 | 4.8
20 | 1 | -1 | 10 | -1 | 1 | 0.4 | 0
21 | 2 | -1 | 10 | 5 | 1 | 1 | 0.4
22 | 3 | -1 | 10 | 6 | 4 | 0.7 | 1.4
23 | 4 | -1 | 10 | -6 | 4 | 0.3 | 2.1
24 | 5 | -1 | 10 | 7 | 8 | 1 | 2.4
25 | 6 | -1 | 10 | 11 | 9 | 1 | 3.4
26 | 7 | -1 | 10 | 16 | 16 | 1 | 4.4
27 | 8 | -1 | 10 | 15 | 3 | 1 | 5.4
28 | 9 | -1 | 10 | 10 | -1 | 0 | 6.4
29 | 1 | -1 | 11 | -1 | 1 | 0.4 | 0
30 | 2 | -1 | 11 | 5 | 1 | 1 | 0.4
31 | 3 | -1 | 11 | 6 | 4 | 0.7 | 1.4
32 | 4 | -1 | 11 | -6 | 4 | 0.3 | 2.1
33 | 5 | -1 | 11 | 7 | 8 | 1 | 2.4
34 | 6 | -1 | 11 | 11 | -1 | 0 | 3.4
35 | 1 | 5 | -6 | 5 | 1 | 1 | 0
36 | 2 | 5 | -6 | 6 | 4 | 0.7 | 1
37 | 3 | 5 | -6 | -6 | -1 | 0 | 1.7
38 | 1 | 5 | -3 | 5 | 1 | 1 | 0
39 | 2 | 5 | -3 | 6 | 4 | 0.7 | 1
40 | 3 | 5 | -3 | -6 | 4 | 0.3 | 1.7
41 | 4 | 5 | -3 | 7 | 10 | 1 | 2
42 | 5 | 5 | -3 | 8 | 12 | 0.6 | 3
43 | 6 | 5 | -3 | -3 | -1 | 0 | 3.6
44 | 1 | 5 | -2 | 5 | 1 | 1 | 0
45 | 2 | 5 | -2 | 6 | 4 | 0.7 | 1
46 | 3 | 5 | -2 | -6 | 4 | 0.3 | 1.7
47 | 4 | 5 | -2 | 7 | 8 | 1 | 2
48 | 5 | 5 | -2 | 11 | 9 | 1 | 3
49 | 6 | 5 | -2 | 16 | 15 | 0.4 | 4
50 | 7 | 5 | -2 | -2 | -1 | 0 | 4.4
51 | 1 | 5 | 10 | 5 | 1 | 1 | 0
52 | 2 | 5 | 10 | 6 | 4 | 0.7 | 1
53 | 3 | 5 | 10 | -6 | 4 | 0.3 | 1.7
54 | 4 | 5 | 10 | 7 | 8 | 1 | 2
55 | 5 | 5 | 10 | 11 | 9 | 1 | 3
56 | 6 | 5 | 10 | 16 | 16 | 1 | 4
57 | 7 | 5 | 10 | 15 | 3 | 1 | 5
58 | 8 | 5 | 10 | 10 | -1 | 0 | 6
59 | 1 | 5 | 11 | 5 | 1 | 1 | 0
60 | 2 | 5 | 11 | 6 | 4 | 0.7 | 1
61 | 3 | 5 | 11 | -6 | 4 | 0.3 | 1.7
62 | 4 | 5 | 11 | 7 | 8 | 1 | 2
63 | 5 | 5 | 11 | 11 | -1 | 0 | 3
(63 rows)
Passes in front or visits with right side driving.¶
For point \(6\) and vertex \(11\).
SELECT (start_pid || ' -> ' || end_pid ||' at ' || path_seq || 'th step')::TEXT AS path_at,
CASE WHEN edge = -1 THEN ' visits'
ELSE ' passes in front of'
END as status,
CASE WHEN node < 0 THEN 'Point'
ELSE 'Vertex'
END as is_a,
abs(node) as id
FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[5, -1], ARRAY[-2, -3, -6, 10, 11],
driving_side => 'r', details => true)
WHERE node IN (-6, 11);
path_at | status | is_a | id
----------------------+---------------------+--------+----
-1 -> -6 at 4th step | visits | Point | 6
-1 -> -3 at 4th step | passes in front of | Point | 6
-1 -> -2 at 4th step | passes in front of | Point | 6
-1 -> -2 at 6th step | passes in front of | Vertex | 11
-1 -> 10 at 4th step | passes in front of | Point | 6
-1 -> 10 at 6th step | passes in front of | Vertex | 11
-1 -> 11 at 4th step | passes in front of | Point | 6
-1 -> 11 at 6th step | visits | Vertex | 11
5 -> -6 at 3th step | visits | Point | 6
5 -> -3 at 3th step | passes in front of | Point | 6
5 -> -2 at 3th step | passes in front of | Point | 6
5 -> -2 at 5th step | passes in front of | Vertex | 11
5 -> 10 at 3th step | passes in front of | Point | 6
5 -> 10 at 5th step | passes in front of | Vertex | 11
5 -> 11 at 3th step | passes in front of | Point | 6
5 -> 11 at 5th step | visits | Vertex | 11
(16 rows)
Passes in front or visits with left side driving.¶
For point \(6\) and vertex \(11\).
SELECT (start_pid || ' => ' || end_pid ||' at ' || path_seq || 'th step')::TEXT AS path_at,
CASE WHEN edge = -1 THEN ' visits'
ELSE ' passes in front of'
END as status,
CASE WHEN node < 0 THEN 'Point'
ELSE 'Vertex'
END as is_a,
abs(node) as id
FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[5, -1], ARRAY[-2, -3, -6, 10, 11],
driving_side => 'l', details => true)
WHERE node IN (-6, 11);
path_at | status | is_a | id
----------------------+---------------------+--------+----
-1 => -6 at 3th step | visits | Point | 6
-1 => -3 at 3th step | passes in front of | Point | 6
-1 => -2 at 3th step | passes in front of | Point | 6
-1 => -2 at 5th step | passes in front of | Vertex | 11
-1 => 10 at 3th step | passes in front of | Point | 6
-1 => 10 at 5th step | passes in front of | Vertex | 11
-1 => 11 at 3th step | passes in front of | Point | 6
-1 => 11 at 5th step | visits | Vertex | 11
5 => -6 at 4th step | visits | Point | 6
5 => -3 at 4th step | passes in front of | Point | 6
5 => -2 at 4th step | passes in front of | Point | 6
5 => -2 at 6th step | passes in front of | Vertex | 11
5 => 10 at 4th step | passes in front of | Point | 6
5 => 10 at 6th step | passes in front of | Vertex | 11
5 => 11 at 4th step | passes in front of | Point | 6
5 => 11 at 6th step | visits | Vertex | 11
(16 rows)
See Also¶
Indices and tables