pgr_trsp_withPoints - Proposed

pgr_trsp_withPoints Routing Vertex/Point with restrictions.

Boost Graph Inside

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 3.4.0

  • New proposed signatures:

    • pgr_trsp_withPoints (One to One)

    • pgr_trsp_withPoints (One to Many)

    • pgr_trsp_withPoints (Many to One)

    • pgr_trsp_withPoints (Many to Many)

    • pgr_trsp_withPoints (Combinations)

Description

Modify the graph to include points defined by points_sql. Using Dijkstra algorithm, find the shortest path(s)

Characteristics:

• Vertices of the graph are:

  • positive when it belongs to the Edges SQL

  • negative when it belongs to the Points SQL

• Driving side can not be b

• 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, [options])

pgr_trsp_withPoints(Edges SQL, Restrictions SQL, Points SQL, start vid, end vids, [options])

pgr_trsp_withPoints(Edges SQL, Restrictions SQL, Points SQL, start vids, end vid, [options])

pgr_trsp_withPoints(Edges SQL, Restrictions SQL, Points SQL, start vids, end vids, [options])

pgr_trsp_withPoints(Edges SQL, Restrictions SQL, Combinations SQL, Points SQL, [options])

options: [directed, driving_side, details]

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, [options])

options: [directed, driving_side, details]

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 |   10 |    1 |      2.4
   6 |        6 |        -1 |      10 |    8 |   12 |  0.6 |      3.4
   7 |        7 |        -1 |      10 |   -3 |   12 |  0.4 |        4
   8 |        8 |        -1 |      10 |   12 |   13 |    1 |      4.4
   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, [options])

options: [directed, driving_side, details]

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, [options])

options: [directed, driving_side, details]

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, [options])

options: [directed, driving_side, details]

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 |   10 |    1 |      2.4
   9 |        4 |        -1 |       1 |    8 |   12 |    1 |      3.4
  10 |        5 |        -1 |       1 |   12 |   13 |    1 |      4.4
  11 |        6 |        -1 |       1 |   17 |   15 |    1 |      5.4
  12 |        7 |        -1 |       1 |   16 |    9 |    1 |      6.4
  13 |        8 |        -1 |       1 |   11 |    8 |    1 |      7.4
  14 |        9 |        -1 |       1 |    7 |    7 |    1 |      8.4
  15 |       10 |        -1 |       1 |    3 |    6 |    1 |      9.4
  16 |       11 |        -1 |       1 |    1 |   -1 |    0 |     10.4
  17 |        1 |         6 |      -3 |    6 |    4 |    1 |        0
  18 |        2 |         6 |      -3 |    7 |   10 |    1 |        1
  19 |        3 |         6 |      -3 |    8 |   12 |  0.6 |        2
  20 |        4 |         6 |      -3 |   -3 |   -1 |    0 |      2.6
  21 |        1 |         6 |       1 |    6 |    4 |    1 |        0
  22 |        2 |         6 |       1 |    7 |   10 |    1 |        1
  23 |        3 |         6 |       1 |    8 |   12 |    1 |        2
  24 |        4 |         6 |       1 |   12 |   13 |    1 |        3
  25 |        5 |         6 |       1 |   17 |   15 |    1 |        4
  26 |        6 |         6 |       1 |   16 |    9 |    1 |        5
  27 |        7 |         6 |       1 |   11 |    8 |    1 |        6
  28 |        8 |         6 |       1 |    7 |    7 |    1 |        7
  29 |        9 |         6 |       1 |    3 |    6 |    1 |        8
  30 |       10 |         6 |       1 |    1 |   -1 |    0 |        9
(30 rows)

Combinations

pgr_trsp_withPoints(Edges SQL, Restrictions SQL, Combinations SQL, Points SQL, [options])

options: [directed, driving_side, details]

RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)

OR EMPTY SET

Example:

From point \(1\) to vertex \(10\) 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 |   10 |    1 |      2.4
   6 |        6 |        -1 |      10 |    8 |   12 |  0.6 |      3.4
   7 |        7 |        -1 |      10 |   -3 |   12 |  0.4 |        4
   8 |        8 |        -1 |      10 |   12 |   13 |    1 |      4.4
   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

Returns set of (seq, path_id, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)

Column	Type	Description
seq	INTEGER	Sequential value starting from 1.
path_id	INTEGER	Path identifier. Has value 1 for the first of a path from start_vid to end_vid.
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.
end_vid	BIGINT	Identifier of the ending vertex.
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.
agg_cost	FLOAT	Aggregate cost from start_vid to node.

Additional Examples

Use pgr_findCloseEdges for points on the fly

Using pgr_findCloseEdges:

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 => 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
(10 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

• TRSP - Family of functions

• withPoints - Category

• Sample Data

Indices and tables

• Index

• Search Page