pgr_withPoints - Proposed¶
Name¶
pgr_withPoints - Returns the shortest path in a graph with additional temporary vertices.
Warning
These are 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.
Synopsis¶
Modify the graph to include points defined by points_sql. Using Dijkstra algorithm, find the shortest path(s)
Characteristics:¶
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: \(O(|start\_vids|∗(V \log V + E))\)
Signature Summary¶
pgr_withPoints(edges_sql, points_sql, start_vid, end_vid)
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)
RETURNS SET OF (seq, path_seq, [start_vid,] [end_vid,] node, edge, cost, agg_cost)
Signatures¶
Minimal Use¶
- The minimal signature:
- Is for a directed graph.
- The driving side is set as b both. So arriving/departing to/from the point(s) can be in any direction.
- No details are given about distance of other points of points_sql query.
pgr_withPoints(edges_sql, points_sql, start_vid, end_vid)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
Example: | From point 1 to point 3 |
---|
SELECT * FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
-1, -3);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 | 1 | -1 | 1 | 0.6 | 0
2 | 2 | 2 | 4 | 1 | 0.6
3 | 3 | 5 | 10 | 1 | 1.6
4 | 4 | 10 | 12 | 0.6 | 2.6
5 | 5 | -3 | -1 | 0 | 3.2
(5 rows)
One to One¶
pgr_withPoints(edges_sql, points_sql, start_vid, end_vid,
directed:=true, driving_side:='b', details:=false)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
Example: | From point 1 to vertex 3 |
---|
SELECT * FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
-1, 3,
details := true);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 | 1 | -1 | 1 | 0.6 | 0
2 | 2 | 2 | 4 | 0.7 | 0.6
3 | 3 | -6 | 4 | 0.3 | 1.3
4 | 4 | 5 | 8 | 1 | 1.6
5 | 5 | 6 | 9 | 1 | 2.6
6 | 6 | 9 | 16 | 1 | 3.6
7 | 7 | 4 | 3 | 1 | 4.6
8 | 8 | 3 | -1 | 0 | 5.6
(8 rows)
One to Many¶
pgr_withPoints(edges_sql, points_sql, start_vid, end_vids,
directed:=true, driving_side:='b', details:=false)
RETURNS SET OF (seq, path_seq, end_vid, node, edge, cost, agg_cost)
Example: | From point 1 to point 3 and vertex 5 |
---|
SELECT * FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
-1, ARRAY[-3,5]);
seq | path_seq | end_pid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
1 | 1 | -3 | -1 | 1 | 0.6 | 0
2 | 2 | -3 | 2 | 4 | 1 | 0.6
3 | 3 | -3 | 5 | 10 | 1 | 1.6
4 | 4 | -3 | 10 | 12 | 0.6 | 2.6
5 | 5 | -3 | -3 | -1 | 0 | 3.2
6 | 1 | 5 | -1 | 1 | 0.6 | 0
7 | 2 | 5 | 2 | 4 | 1 | 0.6
8 | 3 | 5 | 5 | -1 | 0 | 1.6
(8 rows)
Many to One¶
pgr_withPoints(edges_sql, points_sql, start_vids, end_vid,
directed:=true, driving_side:='b', details:=false)
RETURNS SET OF (seq, path_seq, start_vid, node, edge, cost, agg_cost)
Example: | From point 1 and vertex 2 to point 3 |
---|
SELECT * FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[-1,2], -3);
seq | path_seq | start_pid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
1 | 1 | -1 | -1 | 1 | 0.6 | 0
2 | 2 | -1 | 2 | 4 | 1 | 0.6
3 | 3 | -1 | 5 | 10 | 1 | 1.6
4 | 4 | -1 | 10 | 12 | 0.6 | 2.6
5 | 5 | -1 | -3 | -1 | 0 | 3.2
6 | 1 | 2 | 2 | 4 | 1 | 0
7 | 2 | 2 | 5 | 10 | 1 | 1
8 | 3 | 2 | 10 | 12 | 0.6 | 2
9 | 4 | 2 | -3 | -1 | 0 | 2.6
(9 rows)
Many to Many¶
pgr_withPoints(edges_sql, points_sql, start_vids, end_vids,
directed:=true, driving_side:='b', details:=false)
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
Example: | From point 1 and vertex 2 to point 3 and vertex 7 |
---|
SELECT * FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[-1,2], ARRAY[-3,7]);
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 | 2 | 4 | 1 | 0.6
3 | 3 | -1 | -3 | 5 | 10 | 1 | 1.6
4 | 4 | -1 | -3 | 10 | 12 | 0.6 | 2.6
5 | 5 | -1 | -3 | -3 | -1 | 0 | 3.2
6 | 1 | -1 | 7 | -1 | 1 | 0.6 | 0
7 | 2 | -1 | 7 | 2 | 4 | 1 | 0.6
8 | 3 | -1 | 7 | 5 | 7 | 1 | 1.6
9 | 4 | -1 | 7 | 8 | 6 | 1 | 2.6
10 | 5 | -1 | 7 | 7 | -1 | 0 | 3.6
11 | 1 | 2 | -3 | 2 | 4 | 1 | 0
12 | 2 | 2 | -3 | 5 | 10 | 1 | 1
13 | 3 | 2 | -3 | 10 | 12 | 0.6 | 2
14 | 4 | 2 | -3 | -3 | -1 | 0 | 2.6
15 | 1 | 2 | 7 | 2 | 4 | 1 | 0
16 | 2 | 2 | 7 | 5 | 7 | 1 | 1
17 | 3 | 2 | 7 | 8 | 6 | 1 | 2
18 | 4 | 2 | 7 | 7 | -1 | 0 | 3
(18 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 Points SQL query¶
points_sql: | an SQL query, which should return a set of rows with the following columns: |
---|
Column | Type | Description |
---|---|---|
pid | ANY-INTEGER |
|
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 |
|
Where:
ANY-INTEGER: | smallint, int, bigint |
---|---|
ANY-NUMERICAL: | smallint, int, bigint, real, float |
Description of the parameters of the signatures¶
Parameter | Type | Description |
---|---|---|
edges_sql | TEXT | Edges SQL query as described above. |
points_sql | TEXT | Points SQL query as described above. |
start_vid | ANY-INTEGER | Starting vertex identifier. When negative: is a point’s pid. |
end_vid | ANY-INTEGER | Ending vertex identifier. When negative: is a point’s pid. |
start_vids | ARRAY[ANY-INTEGER] | Array of identifiers of starting vertices. When negative: is a point’s pid. |
end_vids | ARRAY[ANY-INTEGER] | Array of identifiers of ending vertices. When negative: is a point’s pid. |
directed | BOOLEAN | (optional). When false the graph is considered as Undirected. Default is true which considers the graph as Directed. |
driving_side | CHAR |
|
details | BOOLEAN | (optional). When true the results will include the points in points_sql that are in the path. Default is false which ignores other points of the points_sql. |
Description of the return values¶
Returns set of (seq, [path_seq,] [start_vid,] [end_vid,] node, edge, cost, agg_cost)
Column | Type | Description |
---|---|---|
seq | INTEGER | Row sequence. |
path_seq | INTEGER | Path sequence that indicates the relative position on the path. |
start_vid | BIGINT | Identifier of the starting vertex. When negative: is a point’s pid. |
end_vid | BIGINT | Identifier of the ending vertex. When negative: is a point’s pid. |
node | BIGINT |
|
edge | BIGINT |
|
cost | FLOAT |
|
agg_cost | FLOAT |
|
Examples¶
Example: | Which path (if any) passes in front of point 6 or vertex 6 with right side driving topology. |
---|
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 edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[1,-1], ARRAY[-2,-3,-6,3,6],
driving_side := 'r',
details := true)
WHERE node IN (-6,6);
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 | 6
(-1 => 3) at 4th step: | passes in front of | Point | 6
(-1 => 3) at 6th step: | passes in front of | Vertex | 6
(-1 => 6) at 4th step: | passes in front of | Point | 6
(-1 => 6) at 6th step: | visits | Vertex | 6
(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 | 6
(1 => 3) at 3th step: | passes in front of | Point | 6
(1 => 3) at 5th step: | passes in front of | Vertex | 6
(1 => 6) at 3th step: | passes in front of | Point | 6
(1 => 6) at 5th step: | visits | Vertex | 6
(16 rows)
Example: | Which path (if any) passes in front of point 6 or vertex 6 with left side driving topology. |
---|
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 edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[1,-1], ARRAY[-2,-3,-6,3,6],
driving_side := 'l',
details := true)
WHERE node IN (-6,6);
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 | 6
(-1 => 3) at 3th step: | passes in front of | Point | 6
(-1 => 3) at 5th step: | passes in front of | Vertex | 6
(-1 => 6) at 3th step: | passes in front of | Point | 6
(-1 => 6) at 5th step: | visits | Vertex | 6
(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 | 6
(1 => 3) at 4th step: | passes in front of | Point | 6
(1 => 3) at 6th step: | passes in front of | Vertex | 6
(1 => 6) at 4th step: | passes in front of | Point | 6
(1 => 6) at 6th step: | visits | Vertex | 6
(16 rows)
Example: | Many to many example with a twist: on undirected graph and showing details. |
---|
SELECT * FROM pgr_withPoints(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[-1,2], ARRAY[-3,7],
directed := false,
details := true);
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 | 2 | 4 | 0.7 | 0.6
3 | 3 | -1 | -3 | -6 | 4 | 0.3 | 1.3
4 | 4 | -1 | -3 | 5 | 10 | 1 | 1.6
5 | 5 | -1 | -3 | 10 | 12 | 0.6 | 2.6
6 | 6 | -1 | -3 | -3 | -1 | 0 | 3.2
7 | 1 | -1 | 7 | -1 | 1 | 0.6 | 0
8 | 2 | -1 | 7 | 2 | 4 | 0.7 | 0.6
9 | 3 | -1 | 7 | -6 | 4 | 0.3 | 1.3
10 | 4 | -1 | 7 | 5 | 7 | 1 | 1.6
11 | 5 | -1 | 7 | 8 | 6 | 0.7 | 2.6
12 | 6 | -1 | 7 | -4 | 6 | 0.3 | 3.3
13 | 7 | -1 | 7 | 7 | -1 | 0 | 3.6
14 | 1 | 2 | -3 | 2 | 4 | 0.7 | 0
15 | 2 | 2 | -3 | -6 | 4 | 0.3 | 0.7
16 | 3 | 2 | -3 | 5 | 10 | 1 | 1
17 | 4 | 2 | -3 | 10 | 12 | 0.6 | 2
18 | 5 | 2 | -3 | -3 | -1 | 0 | 2.6
19 | 1 | 2 | 7 | 2 | 4 | 0.7 | 0
20 | 2 | 2 | 7 | -6 | 4 | 0.3 | 0.7
21 | 3 | 2 | 7 | 5 | 7 | 1 | 1
22 | 4 | 2 | 7 | 8 | 6 | 0.7 | 2
23 | 5 | 2 | 7 | -4 | 6 | 0.3 | 2.7
24 | 6 | 2 | 7 | 7 | -1 | 0 | 3
(24 rows)
The queries use the Sample Data network.
History
- Proposed in version 2.2