pgr_trsp_withPoints - Proposed

pgr_trsp_withPoints Routing Vertex/Point with restrictions.

images/boost-inside.jpeg

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

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:

  • 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     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 , [ 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     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 , [ 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     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

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 => 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