pgr_withPointsVia - Proposed

pgr_withPointsVia - Route that goes through a list of vertices and/or points.

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 3.4.0

    • New proposed function pgr_withPointsVia (One Via)

Description

Given a graph, a set of points on the graphs edges and a list of vertices, this function is equivalent to finding the shortest path between \(vertex_i\) and \(vertex_{i+1}\) (where \(vertex\) can be a vertex or a point on the graph) for all \(i < size\_of(via\;vertices)\).

Route:

is a sequence of paths.

Path:

is a section of the route.

The general algorithm is as follows:

  • Build the Graph with the new points.

    • The points identifiers will be converted to negative values.

    • The vertices identifiers will remain positive.

  • Execute a pgr_dijkstraVia - Proposed.

Signatures

One Via

pgr_withPointsVia(Edges SQL, Points SQL, via vertices, [options])
options: [directed, strict, U_turn_on_edge]
RETURNS SET OF (seq, path_id, path_seq, start_vid, end_vid, node, edge, cost, agg_cost, route_agg_cost)
OR EMPTY SET
Example:

Find the route that visits the vertices \(\{ -6, 15, -1\}\) in that order on a directed graph.

SELECT * FROM pgr_withPointsVia(
  'SELECT id, source, target, cost, reverse_cost FROM edges order by id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  ARRAY[-6, 15, -1]);
 seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost | route_agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------+----------------
   1 |       1 |        1 |        -6 |      15 |   -6 |    4 |  0.3 |        0 |              0
   2 |       1 |        2 |        -6 |      15 |    7 |    8 |    1 |      0.3 |            0.3
   3 |       1 |        3 |        -6 |      15 |   11 |    9 |    1 |      1.3 |            1.3
   4 |       1 |        4 |        -6 |      15 |   16 |   16 |    1 |      2.3 |            2.3
   5 |       1 |        5 |        -6 |      15 |   15 |   -1 |    0 |      3.3 |            3.3
   6 |       2 |        1 |        15 |      -1 |   15 |    3 |    1 |        0 |            3.3
   7 |       2 |        2 |        15 |      -1 |   10 |    2 |    1 |        1 |            4.3
   8 |       2 |        3 |        15 |      -1 |    6 |    1 |  0.6 |        2 |            5.3
   9 |       2 |        4 |        15 |      -1 |   -1 |   -2 |    0 |      2.6 |            5.9
(9 rows)

Parameters

Parameter

Type

Default

Description

Edges SQL

TEXT

SQL query as described.

Points SQL

TEXT

SQL query as described.

via vertices

ARRAY [ ANY-INTEGER ]

Array of ordered vertices identifiers that are going to be visited.

  • When positive it is considered a vertex identifier

  • When negative it is considered a point identifier

Where:

ANY-INTEGER:

SMALLINT, INTEGER, BIGINT

ANY-NUMERICAL:

SMALLINT, INTEGER, BIGINT, REAL, FLOAT

Optional parameters

Column

Type

Default

Description

directed

BOOLEAN

true

  • When true the graph is considered Directed

  • When false the graph is considered as Undirected.

Via optional parameters

Parameter

Type

Default

Description

strict

BOOLEAN

false

  • When true if a path is missing stops and returns EMPTY SET

  • When false ignores missing paths returning all paths found

U_turn_on_edge

BOOLEAN

true

  • When true departing from a visited vertex will not try to avoid

With points optional parameters

Parameter

Type

Default

Description

driving_side

CHAR

b

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

  • r for right driving side.

  • l for left driving side.

  • b for both.

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

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

Result Columns

Column

Type

Description

seq

INTEGER

Sequential value starting from 1.

path_id

INTEGER

Identifier of a path. Has value 1 for the first path.

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.

  • -2 for the last node of the route.

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.

route_agg_cost

FLOAT

Total cost from start_vid of seq = 1 to end_vid of the current seq.

Note

When start_vid, end_vid and node columns have negative values, the identifier is for a Point.

Additional Examples

Use pgr_findCloseEdges in the Points SQL

Visit from vertex \(1\) to the two locations on the graph of point (2.9, 1.8) in order of closeness to the graph.

SELECT * FROM pgr_withPointsVia(
  $e$ SELECT * FROM edges $e$,
  $p$ 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)
  $p$,
  ARRAY[1, -1, -2], details => true);
 seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost | route_agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------+----------------
   1 |       1 |        1 |         1 |      -1 |    1 |    6 |    1 |        0 |              0
   2 |       1 |        2 |         1 |      -1 |    3 |    7 |    1 |        1 |              1
   3 |       1 |        3 |         1 |      -1 |    7 |    8 |  0.9 |        2 |              2
   4 |       1 |        4 |         1 |      -1 |   -2 |    8 |  0.1 |      2.9 |            2.9
   5 |       1 |        5 |         1 |      -1 |   11 |    9 |    1 |        3 |              3
   6 |       1 |        6 |         1 |      -1 |   16 |   16 |    1 |        4 |              4
   7 |       1 |        7 |         1 |      -1 |   15 |    3 |    1 |        5 |              5
   8 |       1 |        8 |         1 |      -1 |   10 |    5 |  0.8 |        6 |              6
   9 |       1 |        9 |         1 |      -1 |   -1 |   -1 |    0 |      6.8 |            6.8
  10 |       2 |        1 |        -1 |      -2 |   -1 |    5 |  0.2 |        0 |            6.8
  11 |       2 |        2 |        -1 |      -2 |   11 |    8 |  0.1 |      0.2 |              7
  12 |       2 |        3 |        -1 |      -2 |   -2 |   -2 |    0 |      0.3 |            7.1
(12 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).

  • Point \(-2\) is visited on the route to from vertex \(1\) to Point \(-1\) (See row where \(seq = 4\)).

Usage variations

All this examples are about the route that visits the vertices \(\{-1, 7, -3, 16, 15\}\) in that order on a directed graph.

SELECT * FROM pgr_withPointsVia(
  'SELECT id, source, target, cost, reverse_cost FROM edges order by id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  ARRAY[-1, 7, -3, 16, 15]);
 seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost | route_agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------+----------------
   1 |       1 |        1 |        -1 |       7 |   -1 |    1 |  0.6 |        0 |              0
   2 |       1 |        2 |        -1 |       7 |    6 |    4 |    1 |      0.6 |            0.6
   3 |       1 |        3 |        -1 |       7 |    7 |   -1 |    0 |      1.6 |            1.6
   4 |       2 |        1 |         7 |      -3 |    7 |   10 |    1 |        0 |            1.6
   5 |       2 |        2 |         7 |      -3 |    8 |   12 |  0.6 |        1 |            2.6
   6 |       2 |        3 |         7 |      -3 |   -3 |   -1 |    0 |      1.6 |            3.2
   7 |       3 |        1 |        -3 |      16 |   -3 |   12 |  0.4 |        0 |            3.2
   8 |       3 |        2 |        -3 |      16 |   12 |   13 |    1 |      0.4 |            3.6
   9 |       3 |        3 |        -3 |      16 |   17 |   15 |    1 |      1.4 |            4.6
  10 |       3 |        4 |        -3 |      16 |   16 |   -1 |    0 |      2.4 |            5.6
  11 |       4 |        1 |        16 |      15 |   16 |   16 |    1 |        0 |            5.6
  12 |       4 |        2 |        16 |      15 |   15 |   -2 |    0 |        1 |            6.6
(12 rows)

Aggregate cost of the third path.

SELECT agg_cost FROM  pgr_withPointsVia(
  'SELECT id, source, target, cost, reverse_cost FROM edges order by id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  ARRAY[-1, 7, -3, 16, 15])
WHERE path_id = 3 AND edge < 0;
 agg_cost
----------
      2.4
(1 row)

Route’s aggregate cost of the route at the end of the third path.

SELECT route_agg_cost FROM  pgr_withPointsVia(
  'SELECT id, source, target, cost, reverse_cost FROM edges order by id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  ARRAY[-1, 7, -3, 16, 15])
WHERE path_id = 3 AND edge < 0;
 route_agg_cost
----------------
            5.6
(1 row)

Nodes visited in the route.

SELECT row_number() over () as node_seq, node
FROM  pgr_withPointsVia(
  'SELECT id, source, target, cost, reverse_cost FROM edges order by id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  ARRAY[-1, 7, -3, 16, 15])
WHERE edge <> -1 ORDER BY seq;
 node_seq | node
----------+------
        1 |   -1
        2 |    6
        3 |    7
        4 |    8
        5 |   -3
        6 |   12
        7 |   17
        8 |   16
        9 |   15
(9 rows)

The aggregate costs of the route when the visited vertices are reached.

SELECT path_id, route_agg_cost FROM  pgr_withPointsVia(
  'SELECT id, source, target, cost, reverse_cost FROM edges order by id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  ARRAY[-1, 7, -3, 16, 15])
WHERE edge < 0;
 path_id | route_agg_cost
---------+----------------
       1 |            1.6
       2 |            3.2
       3 |            5.6
       4 |            6.6
(4 rows)

Status of “passes in front” or “visits” of the nodes and points.

SELECT seq, node,
CASE WHEN edge = -1 THEN 'visits'
ELSE 'passes in front'
END as status
FROM  pgr_withPointsVia(
  'SELECT id, source, target, cost, reverse_cost FROM edges order by id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  ARRAY[-1, 7, -3, 16, 15], details => true)
WHERE agg_cost <> 0 or seq = 1;
 seq | node |     status
-----+------+-----------------
   1 |   -1 | passes in front
   2 |    6 | passes in front
   3 |   -6 | passes in front
   4 |    7 | visits
   6 |    8 | passes in front
   7 |   -3 | visits
   9 |   12 | passes in front
  10 |   17 | passes in front
  11 |   -2 | passes in front
  12 |   16 | visits
  14 |   15 | passes in front
(11 rows)

See Also

Indices and tables