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)
- New proposed function:
- 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
pgr_withPoints(Edges SQL, Points SQL, start vid, end vid [, directed] [, driving_side] [, details]) pgr_withPoints(Edges SQL, Points SQL, start vid, end vids [, directed] [, driving_side] [, details]) pgr_withPoints(Edges SQL, Points SQL, start vids, end vid [, directed] [, driving_side] [, details]) pgr_withPoints(Edges SQL, Points SQL, start vids, end vids [, directed] [, driving_side] [, details]) pgr_withPoints(Edges SQL, Points SQL, Combinations SQL [, directed] [, driving_side] [, details]) RETURNS (seq, path_seq, [start_vid,] [end_vid,] node, edge, cost, agg_cost)
One to One¶
pgr_withPoints(Edges SQL, Points SQL, start vid, end vid [, directed] [, driving_side] [, details]) RETURNS (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¶
pgr_withPoints(Edges SQL, Points SQL, start vid, end vids [, directed] [, driving_side] [, details]) RETURNS (seq, path_seq, end_vid, 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¶
pgr_withPoints(Edges SQL, Points SQL, start vids, end vid [, directed] [, driving_side] [, details]) RETURNS (seq, path_seq, start_vid, 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¶
pgr_withPoints(Edges SQL, Points SQL, start vids, end vids [, directed] [, driving_side] [, details]) RETURNS (seq, path_seq, start_vid, end_vid, 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¶
pgr_withPoints(Edges SQL, Points SQL, Combinations SQL, [, directed] [, driving_side] [, details]) RETURNS (seq, path_seq, start_vid, end_vid, 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 | TEXT |
Edges SQL as described below |
Points SQL | TEXT |
Points SQL as described below |
Combinations SQL | TEXT |
Combinations SQL as described below |
start vid | BIGINT |
Identifier of the starting vertex of the path. Negative value is for point’s identifier. |
start vids | ARRAY[BIGINT] |
Array of identifiers of starting vertices. Negative values are for point’s identifiers. |
end vid | BIGINT |
Identifier of the ending vertex of the path. Negative value is for point’s identifier. |
end vids | ARRAY[BIGINT] |
Array of identifiers of ending vertices. Negative values are for point’s identifiers. |
Optional parameters¶
Column | Type | Default | Description |
---|---|---|---|
directed |
BOOLEAN |
true |
|
With points optional parameters¶
Parameter | Type | Default | Description |
---|---|---|---|
driving_side |
CHAR |
b |
Value in [
|
details |
BOOLEAN |
false |
|
Inner Queries¶
Edges SQL¶
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 ) |
|
reverse_cost |
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 |
---|---|---|---|
pid |
ANY-INTEGER | value | Identifier of the point.
|
edge_id |
ANY-INTEGER | Identifier of the “closest” edge to the point. | |
fraction |
ANY-NUMERICAL | Value in <0,1> that indicates the relative postition from the first end point of the edge. | |
side |
CHAR |
b |
Value in [
|
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¶
Returns set of (seq, path_seq [, start_pid] [, end_pid], node, edge, cost,
agg_cost)
Column | Type | Description |
---|---|---|
seq |
INTEGER |
Sequential value starting from 1. |
path_seq |
INTEGER |
Relative position in the path.
|
start_pid |
BIGINT |
Identifier of a starting vertex/point of the path.
|
end_pid |
BIGINT |
Identifier of an ending vertex/point of the path.
|
node |
BIGINT |
Identifier of the node in the path from
|
edge |
BIGINT |
Identifier of the edge used to go from
|
cost |
FLOAT |
Cost to traverse from
|
agg_cost |
FLOAT |
Aggregate cost from
|
Additional Examples¶
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