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.

_images/boost-inside.jpeg

Boost Graph Inside

Availability

  • Version 2.2.0

    • New proposed function

Support

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, from_vid,  to_vid  [, directed] [, driving_side] [, details])
pgr_withPoints(edges_sql, points_sql, from_vid,  to_vids [, directed] [, driving_side] [, details])
pgr_withPoints(edges_sql, points_sql, from_vids, to_vid  [, directed] [, driving_side] [, details])
pgr_withPoints(edges_sql, points_sql, from_vids, to_vids [, directed] [, driving_side] [, details])
RETURNS SET OF (seq, path_seq, [start_vid,] [end_vid,] node, edge, cost, agg_cost)

Using defaults

pgr_withPoints(edges_sql, points_sql, from_vid, to_vid)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
Example

From point \(1\) to point \(3\)

  • 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.

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, from_vid,  to_vid  [, directed] [, driving_side] [, details])
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
Example

From point \(1\) to vertex \(3\) with details of passing points

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, from_vid,  to_vids [, directed] [, driving_side] [, details])
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, from_vids, to_vid  [, directed] [, driving_side] [, details])
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, from_vids, to_vids [, directed] [, driving_side] [, details])
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)

Parameters

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.

Inner query

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

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

(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

ANY-NUMERICAL

smallint, int, bigint, real, float

Result Columns

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.

Additional 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

From point \(1\) and vertex \(2\) to point \(3\) to vertex \(7\) on an undirected graph, with 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