pgr_trsp_withPoints - Proposed

pgr_trsp_withPoints Routing Vertex/Point with restrictions.

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

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.

  • Driving side can not be b (both)

  • Vertices of the graph are:

  • 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_trsp_withPoints(Edges SQL, Restrictions SQL, Points SQL, start vid,  end vid
                          [, directed], [, driving_side] [, details]) -- Proposed on v3.4
pgr_trsp_withPoints(Edges SQL, Restrictions SQL, Points SQL, start vid,  end vids
                          [, directed], [, driving_side] [, details]) -- Proposed on v3.4
pgr_trsp_withPoints(Edges SQL, Restrictions SQL, Points SQL, start vids, end vid
                          [, directed], [, driving_side] [, details]) -- Proposed on v3.4
pgr_trsp_withPoints(Edges SQL, Restrictions SQL, Points SQL, start vids, end vids
                          [, directed], [, driving_side] [, details]) -- Proposed on v3.4
pgr_trsp_withPoints(Edges SQL, Restrictions SQL, Combinations SQL, Points SQL,
                          [, directed], [, driving_side] [, details]) -- Proposed on v3.4
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET

One to One

pgr_trsp_withPoints(Edges SQL, Restrictions SQL, Points SQL, start vid,  end vid
                          [, directed], [, driving_side] [, details]) -- Proposed on v3.4
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example:

From point \(1\) to vertex \(10\) with details on a left driving side configuration on a directed graph with details.

SELECT * FROM pgr_trsp_withPoints(
  $$SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id$$,
  $$SELECT id, path, cost FROM restrictions$$,
  $$SELECT pid, edge_id, fraction, side FROM pointsOfInterest$$,
  -1, 10,
  details => true);
 seq | path_seq | start_vid | end_vid | 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 |   15 |  0.4 |      4.4
   8 |        8 |        -1 |      10 |   -2 |   15 |  0.6 |      4.8
   9 |        9 |        -1 |      10 |   17 |   15 |    1 |      5.4
  10 |       10 |        -1 |      10 |   16 |   16 |    1 |      6.4
  11 |       11 |        -1 |      10 |   15 |    3 |    1 |      7.4
  12 |       12 |        -1 |      10 |   10 |   -1 |    0 |      8.4
(12 rows)

One to Many

pgr_trsp_withPoints(Edges SQL, Restrictions SQL, Points SQL, start vid, end vids
                          [, directed], [, driving_side] [, details]) -- Proposed on v3.4
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example:

From point \(1\) to point \(3\) and vertex \(7\).

SELECT * FROM pgr_trsp_withPoints(
  $$SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id$$,
  $$SELECT id, path, cost FROM restrictions$$,
  $$SELECT pid, edge_id, fraction, side FROM pointsOfInterest$$,
  -1, ARRAY[-3, 7]);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |        -1 |      -3 |   -1 |    1 |  1.4 |        0
   2 |        2 |        -1 |      -3 |    6 |    4 |    1 |      1.4
   3 |        3 |        -1 |      -3 |    7 |   10 |    1 |      2.4
   4 |        4 |        -1 |      -3 |    8 |   12 |  0.6 |      3.4
   5 |        5 |        -1 |      -3 |   -3 |   -1 |    0 |        4
   6 |        1 |        -1 |       7 |   -1 |    1 |  1.4 |        0
   7 |        2 |        -1 |       7 |    6 |    4 |    1 |      1.4
   8 |        3 |        -1 |       7 |    7 |   -1 |    0 |      2.4
(8 rows)

Many to One

pgr_trsp_withPoints(Edges SQL, Restrictions SQL, Points SQL, start vids, end vid
                          [, directed], [, driving_side] [, details]) -- Proposed on v3.4
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example:

From point \(1\) and vertex \(6\) to point \(3\).

SELECT * FROM pgr_trsp_withPoints(
  $$SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id$$,
  $$SELECT id, path, cost FROM restrictions$$,
  $$SELECT pid, edge_id, fraction, side FROM pointsOfInterest$$,
  ARRAY[-1, 6], -3);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |        -1 |      -3 |   -1 |    1 |  1.4 |        0
   2 |        2 |        -1 |      -3 |    6 |    4 |    1 |      1.4
   3 |        3 |        -1 |      -3 |    7 |   10 |    1 |      2.4
   4 |        4 |        -1 |      -3 |    8 |   12 |  0.6 |      3.4
   5 |        5 |        -1 |      -3 |   -3 |   -1 |    0 |        4
   6 |        1 |         6 |      -3 |    6 |    4 |    1 |        0
   7 |        2 |         6 |      -3 |    7 |   10 |    1 |        1
   8 |        3 |         6 |      -3 |    8 |   12 |  0.6 |        2
   9 |        4 |         6 |      -3 |   -3 |   -1 |    0 |      2.6
(9 rows)

Many to Many

pgr_trsp_withPoints(Edges SQL, Restrictions SQL, Points SQL, start vids, end vids
                          [, directed], [, driving_side] [, details]) -- Proposed on v3.4
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example:

From point \(1\) and vertex \(6\) to point \(3\) and vertex \(1\).

SELECT * FROM pgr_trsp_withPoints(
  $$SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id$$,
  $$SELECT id, path, cost FROM restrictions$$,
  $$SELECT pid, edge_id, fraction, side FROM pointsOfInterest$$,
  ARRAY[-1, 6], ARRAY[-3, 1]);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |        -1 |      -3 |   -1 |    1 |  1.4 |        0
   2 |        2 |        -1 |      -3 |    6 |    4 |    1 |      1.4
   3 |        3 |        -1 |      -3 |    7 |   10 |    1 |      2.4
   4 |        4 |        -1 |      -3 |    8 |   12 |  0.6 |      3.4
   5 |        5 |        -1 |      -3 |   -3 |   -1 |    0 |        4
   6 |        1 |        -1 |       1 |   -1 |    1 |  1.4 |        0
   7 |        2 |        -1 |       1 |    6 |    4 |    1 |      1.4
   8 |        3 |        -1 |       1 |    7 |    8 |    1 |      2.4
   9 |        4 |        -1 |       1 |   11 |    9 |    1 |      3.4
  10 |        5 |        -1 |       1 |   16 |   15 |    2 |      4.4
  11 |        6 |        -1 |       1 |   16 |    9 |    1 |      6.4
  12 |        7 |        -1 |       1 |   11 |    8 |    1 |      7.4
  13 |        8 |        -1 |       1 |    7 |    7 |    1 |      8.4
  14 |        9 |        -1 |       1 |    3 |    6 |    1 |      9.4
  15 |       10 |        -1 |       1 |    1 |   -1 |    0 |     10.4
  16 |        1 |         6 |      -3 |    6 |    4 |    1 |        0
  17 |        2 |         6 |      -3 |    7 |   10 |    1 |        1
  18 |        3 |         6 |      -3 |    8 |   12 |  0.6 |        2
  19 |        4 |         6 |      -3 |   -3 |   -1 |    0 |      2.6
  20 |        1 |         6 |       1 |    6 |    4 |    1 |        0
  21 |        2 |         6 |       1 |    7 |   10 |    1 |        1
  22 |        3 |         6 |       1 |    8 |   12 |    1 |        2
  23 |        4 |         6 |       1 |   12 |   13 |    1 |        3
  24 |        5 |         6 |       1 |   17 |   15 |    1 |        4
  25 |        6 |         6 |       1 |   16 |    9 |    1 |        5
  26 |        7 |         6 |       1 |   11 |    8 |    1 |        6
  27 |        8 |         6 |       1 |    7 |    7 |    1 |        7
  28 |        9 |         6 |       1 |    3 |    6 |    1 |        8
  29 |       10 |         6 |       1 |    1 |   -1 |    0 |        9
(29 rows)

Combinations

pgr_trsp_withPoints(Edges SQL, Restrictions SQL, Combinations SQL, Points SQL,
                          [, directed], [, driving_side] [, details]) -- Proposed on v3.4
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
Example:

From point \(1\) to vertex \(10\) and from vertex \(6\) to point \(3\) with right side driving configuration.

SELECT * FROM pgr_trsp_withPoints(
  $$SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id$$,
  $$SELECT id, path, cost FROM restrictions$$,
  $$SELECT pid, edge_id, fraction, side FROM pointsOfInterest$$,
  $$SELECT * FROM (VALUES (-1, 10), (6, -3)) AS t(source, target)$$,
  driving_side => 'r',
  details => true);
 seq | path_seq | start_vid | end_vid | 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 |   15 |  0.4 |      4.4
   8 |        8 |        -1 |      10 |   -2 |   15 |  0.6 |      4.8
   9 |        9 |        -1 |      10 |   17 |   15 |    1 |      5.4
  10 |       10 |        -1 |      10 |   16 |   16 |    1 |      6.4
  11 |       11 |        -1 |      10 |   15 |    3 |    1 |      7.4
  12 |       12 |        -1 |      10 |   10 |   -1 |    0 |      8.4
  13 |        1 |         6 |      -3 |    6 |    4 |  0.7 |        0
  14 |        2 |         6 |      -3 |   -6 |    4 |  0.3 |      0.7
  15 |        3 |         6 |      -3 |    7 |   10 |    1 |        1
  16 |        4 |         6 |      -3 |    8 |   12 |  0.6 |        2
  17 |        5 |         6 |      -3 |   -3 |   -1 |    0 |      2.6
(17 rows)

Parameters

Column

Type

Description

Edges SQL

TEXT

SQL query as described.

Restrictions SQL

TEXT

SQL query as described.

Combinations SQL

TEXT

Combinations SQL as described below

start vid

ANY-INTEGER

Identifier of the departure vertex.

start vids

ARRAY[ ANY-INTEGER ]

Array of identifiers of destination vertices.

end vid

ANY-INTEGER

Identifier of the departure vertex.

end vids

ARRAY[ ANY-INTEGER ]

Array of identifiers of destination vertices.

Where:

ANY-INTEGER:

SMALLINT, INTEGER, BIGINT

Optional parameters

Column

Type

Default

Description

directed

BOOLEAN

true

  • When true the graph is considered Directed

  • When false the graph is considered as Undirected.

With points optional parameters

Parameter

Type

Default

Description

driving_side

CHAR

r

Value in [r, l] indicating if the driving side is:

  • r for right driving side

  • l for left driving side

  • Any other value will be considered as r

details

BOOLEAN

false

  • When true the results will include the points that are in the path.

  • When false the results will not include the points that are in the path.


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 (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

Restrictions SQL

Column

Type

Description

path

ARRAY[ ANY-INTEGER ]

Sequence of edge identifiers that form a path that is not allowed to be taken. - Empty arrays or NULL arrays are ignored. - Arrays that have a NULL element will raise an exception.

Cost

ANY-NUMERICAL

Cost of taking the forbidden path.

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.

  • Use with positive value, as internally will be converted to negative value

  • If column is present, it can not be NULL.

  • If column is not present, a sequential negative value 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

b

Value in [b, r, l, NULL] indicating if the point is:

  • In the right r,

  • In the left l,

  • In both sides b, NULL

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

Column

Type

Description

seq

INTEGER

Sequential value starting from 1.

path_seq

INTEGER

Relative position in the path. Has value 1 for the beginning of a path.

start_vid

BIGINT

Identifier of the starting vertex of the path.

end_vid

BIGINT

Identifier of the ending vertex of the path.

node

BIGINT

Identifier of the node in the path from start_vid to end_vid.

edge

BIGINT

Identifier of the edge used to go from node to the next node in the path sequence.

  • -1 for the last node of the path.

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_vid to node.

  • 0 for the first row in the path sequence.

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_trsp_withPoints(
  $e$ SELECT * FROM edges $e$,
  $r$ SELECT id, path, cost FROM restrictions $r$,
  $p$ 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],
  driving_side => 'r');
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         1 |      -2 |    1 |    6 |    1 |        0
   2 |        2 |         1 |      -2 |    3 |    7 |    1 |        1
   3 |        3 |         1 |      -2 |    7 |    8 |  0.9 |        2
   4 |        4 |         1 |      -2 |   -2 |   -1 |    0 |      2.9
   5 |        1 |         1 |      -1 |    1 |    6 |    1 |        0
   6 |        2 |         1 |      -1 |    3 |    7 |    1 |        1
   7 |        3 |         1 |      -1 |    7 |    8 |    2 |        2
   8 |        4 |         1 |      -1 |    7 |   10 |    1 |        4
   9 |        5 |         1 |      -1 |    8 |   12 |    1 |        5
  10 |        6 |         1 |      -1 |   12 |   13 |    1 |        6
  11 |        7 |         1 |      -1 |   17 |   15 |    1 |        7
  12 |        8 |         1 |      -1 |   16 |   16 |    1 |        8
  13 |        9 |         1 |      -1 |   15 |    3 |    1 |        9
  14 |       10 |         1 |      -1 |   10 |    5 |  0.8 |       10
  15 |       11 |         1 |      -1 |   -1 |   -1 |    0 |     10.8
(15 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).

Pass in front or visits

Which path (if any) passes in front of point \(6\) or vertex \(11\) with right side driving topology.

SELECT ('(' || start_vid || ' => ' || end_vid ||') 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_trsp_withPoints(
    $$SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id$$,
    $$SELECT id, path, cost FROM restrictions$$,
    $$SELECT pid, edge_id, fraction, side FROM pointsOfInterest$$,
    ARRAY[5, -1], ARRAY[-6, -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 => 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 => 10) at 3th step:  |  passes in front of | Point  |  6
 (5 => 11) at 3th step:  |  passes in front of | Point  |  6
 (5 => 11) at 5th step:  |  visits             | Vertex | 11
(11 rows)

Show details on undirected graph

From point \(1\) and vertex \(6\) to point \(3\) to vertex \(1\) on an undirected graph, with details.

SELECT * FROM pgr_trsp_withPoints(
  $$SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id$$,
  $$SELECT id, path, cost FROM restrictions$$,
  $$SELECT pid, edge_id, fraction, side FROM pointsOfInterest$$,
  ARRAY[-1, 6], ARRAY[-3, 1],
  directed => false,
  details => true);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |        -1 |      -3 |   -1 |    1 |  0.6 |        0
   2 |        2 |        -1 |      -3 |    6 |    4 |  0.7 |      0.6
   3 |        3 |        -1 |      -3 |   -6 |    4 |  0.3 |      1.3
   4 |        4 |        -1 |      -3 |    7 |   10 |    1 |      1.6
   5 |        5 |        -1 |      -3 |    8 |   12 |  0.6 |      2.6
   6 |        6 |        -1 |      -3 |   -3 |   -1 |    0 |      3.2
   7 |        1 |        -1 |       1 |   -1 |    1 |  0.6 |        0
   8 |        2 |        -1 |       1 |    6 |    4 |  0.7 |      0.6
   9 |        3 |        -1 |       1 |   -6 |    4 |  0.3 |      1.3
  10 |        4 |        -1 |       1 |    7 |    7 |    1 |      1.6
  11 |        5 |        -1 |       1 |    3 |    6 |  0.7 |      2.6
  12 |        6 |        -1 |       1 |   -4 |    6 |  0.3 |      3.3
  13 |        7 |        -1 |       1 |    1 |   -1 |    0 |      3.6
  14 |        1 |         6 |      -3 |    6 |    4 |  0.7 |        0
  15 |        2 |         6 |      -3 |   -6 |    4 |  0.3 |      0.7
  16 |        3 |         6 |      -3 |    7 |   10 |    1 |        1
  17 |        4 |         6 |      -3 |    8 |   12 |  0.6 |        2
  18 |        5 |         6 |      -3 |   -3 |   -1 |    0 |      2.6
  19 |        1 |         6 |       1 |    6 |    4 |  0.7 |        0
  20 |        2 |         6 |       1 |   -6 |    4 |  0.3 |      0.7
  21 |        3 |         6 |       1 |    7 |    7 |    1 |        1
  22 |        4 |         6 |       1 |    3 |    6 |  0.7 |        2
  23 |        5 |         6 |       1 |   -4 |    6 |  0.3 |      2.7
  24 |        6 |         6 |       1 |    1 |   -1 |    0 |        3
(24 rows)

See Also

Indices and tables