# pgr_withPoints - Proposed¶

## Name¶

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: 2.2.0

## 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: $$O(|start\_vids|\times(V \log V + E))$$

## 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¶

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

Weight of the edge (source, target)

• When negative: edge (source, target) does not exist, therefore it’s not part of the graph.
reverse_cost ANY-NUMERICAL -1

Weight of the edge (target, source),

• When negative: edge (target, source) does not exist, therefore it’s not part of the graph.

Where:

ANY-INTEGER: SMALLINT, INTEGER, BIGINT 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

(optional) Identifier of the point.

• If column present, it can not be NULL.
• If column not present, a sequential identifier will be given automatically.
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

(optional) Value in [‘b’, ‘r’, ‘l’, NULL] indicating if the point is:

• In the right, left of the edge or
• If it doesn’t matter with ‘b’ or NULL.
• If column not present ‘b’ is considered.

Where:

ANY-INTEGER: smallint, int, bigint 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
(optional) Value in [‘b’, ‘r’, ‘l’, NULL] indicating if the driving side is:
• In the right or left or
• If it doesn’t matter with ‘b’ or NULL.
• If column not present ‘b’ is considered.
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
Identifier of the node:
• A positive value indicates the node is a vertex of edges_sql.
• A negative value indicates the node is a point of points_sql.
edge BIGINT
Identifier of the edge used to go from node to the next node in the path sequence.
• -1 for the last row in the path sequence.
cost FLOAT
Cost to traverse from node using edge to the next node in the path sequence.
• 0 for the last row in the path sequence.
agg_cost FLOAT
Aggregate cost from start_pid to node.
• 0 for the first row in the path sequence.

## 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