pgr_dijkstraVia - Proposed

pgr_dijkstraVia — Route that goes through a list of 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

Description

Given a list of vertices and a graph, this function is equivalent to finding the shortest path between \(vertex_i\) and \(vertex_{i+1}\) for all \(i < size\_of(via\;vertices)\).

Route:

is a sequence of paths.

Path:

is a section of the route.

Signatures

One Via

pgr_dijkstraVia(Edges SQL, via vertices
           [, directed] [, strict] [, U_turn_on_edge]) - Proposed on v2.2
RETURNS SET OF (seq, path_pid, 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 \(\{5, 1, 8\}\) in that order on an directed graph.

SELECT * FROM pgr_dijkstraVia(
  'SELECT id, source, target, cost, reverse_cost FROM edges order by id',
  ARRAY[5, 1, 8]);
 seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost | route_agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------+----------------
   1 |       1 |        1 |         5 |       1 |    5 |    1 |    1 |        0 |              0
   2 |       1 |        2 |         5 |       1 |    6 |    4 |    1 |        1 |              1
   3 |       1 |        3 |         5 |       1 |    7 |    7 |    1 |        2 |              2
   4 |       1 |        4 |         5 |       1 |    3 |    6 |    1 |        3 |              3
   5 |       1 |        5 |         5 |       1 |    1 |   -1 |    0 |        4 |              4
   6 |       2 |        1 |         1 |       8 |    1 |    6 |    1 |        0 |              4
   7 |       2 |        2 |         1 |       8 |    3 |    7 |    1 |        1 |              5
   8 |       2 |        3 |         1 |       8 |    7 |   10 |    1 |        2 |              6
   9 |       2 |        4 |         1 |       8 |    8 |   -2 |    0 |        3 |              7
(9 rows)

Parameters

Parameter

Type

Default

Description

Edges SQL

TEXT

SQL query as described.

via vertices

ARRAY[ ANY-INTEGER ]

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

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

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

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.

Additional Examples

All this examples are about the route that visits the vertices \(\{5, 7, 1, 8, 15\}\) in that order on a directed graph.

The main query

SELECT * FROM pgr_dijkstraVia(
  'SELECT id, source, target, cost, reverse_cost FROM edges order by id',
  ARRAY[5, 7, 1, 8, 15]);
 seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost | route_agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------+----------------
   1 |       1 |        1 |         5 |       7 |    5 |    1 |    1 |        0 |              0
   2 |       1 |        2 |         5 |       7 |    6 |    4 |    1 |        1 |              1
   3 |       1 |        3 |         5 |       7 |    7 |   -1 |    0 |        2 |              2
   4 |       2 |        1 |         7 |       1 |    7 |    7 |    1 |        0 |              2
   5 |       2 |        2 |         7 |       1 |    3 |    6 |    1 |        1 |              3
   6 |       2 |        3 |         7 |       1 |    1 |   -1 |    0 |        2 |              4
   7 |       3 |        1 |         1 |       8 |    1 |    6 |    1 |        0 |              4
   8 |       3 |        2 |         1 |       8 |    3 |    7 |    1 |        1 |              5
   9 |       3 |        3 |         1 |       8 |    7 |   10 |    1 |        2 |              6
  10 |       3 |        4 |         1 |       8 |    8 |   -1 |    0 |        3 |              7
  11 |       4 |        1 |         8 |      15 |    8 |   12 |    1 |        0 |              7
  12 |       4 |        2 |         8 |      15 |   12 |   13 |    1 |        1 |              8
  13 |       4 |        3 |         8 |      15 |   17 |   15 |    1 |        2 |              9
  14 |       4 |        4 |         8 |      15 |   16 |   16 |    1 |        3 |             10
  15 |       4 |        5 |         8 |      15 |   15 |   -2 |    0 |        4 |             11
(15 rows)

Aggregate cost of the third path.

SELECT agg_cost FROM pgr_dijkstraVia(
  'SELECT id, source, target, cost, reverse_cost FROM edges order by id',
  ARRAY[5, 7, 1, 8, 15])
WHERE path_id = 3 AND edge <0;
 agg_cost
----------
        3
(1 row)

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

SELECT route_agg_cost FROM pgr_dijkstraVia(
  'SELECT id, source, target, cost, reverse_cost FROM edges order by id',
  ARRAY[5, 7, 1, 8, 15])
WHERE path_id = 3 AND edge < 0;
 route_agg_cost
----------------
              7
(1 row)

Nodes visited in the route.

SELECT row_number() over () as node_seq, node
FROM  pgr_dijkstraVia(
  'SELECT id, source, target, cost, reverse_cost FROM edges order by id',
  ARRAY[5, 7, 1, 8, 15])
WHERE edge <> -1 ORDER BY seq;
 node_seq | node
----------+------
        1 |    5
        2 |    6
        3 |    7
        4 |    3
        5 |    1
        6 |    3
        7 |    7
        8 |    8
        9 |   12
       10 |   17
       11 |   16
       12 |   15
(12 rows)

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

SELECT path_id, route_agg_cost FROM  pgr_dijkstraVia(
  'SELECT id, source, target, cost, reverse_cost FROM edges order by id',
  ARRAY[5, 7, 1, 8, 15])
WHERE edge < 0;
 path_id | route_agg_cost
---------+----------------
       1 |              2
       2 |              4
       3 |              7
       4 |             11
(4 rows)

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

SELECT seq, route_agg_cost, node, agg_cost ,
  CASE WHEN edge = -1 THEN 'visits'
  ELSE 'passes in front'
  END as status
FROM  pgr_dijkstraVia(
  'SELECT id, source, target, cost, reverse_cost FROM edges order by id',
  ARRAY[5, 7, 1, 8, 15])
WHERE agg_cost  <> 0 or seq = 1;
 seq | route_agg_cost | node | agg_cost |     status
-----+----------------+------+----------+-----------------
   1 |              0 |    5 |        0 | passes in front
   2 |              1 |    6 |        1 | passes in front
   3 |              2 |    7 |        2 | visits
   5 |              3 |    3 |        1 | passes in front
   6 |              4 |    1 |        2 | visits
   8 |              5 |    3 |        1 | passes in front
   9 |              6 |    7 |        2 | passes in front
  10 |              7 |    8 |        3 | visits
  12 |              8 |   12 |        1 | passes in front
  13 |              9 |   17 |        2 | passes in front
  14 |             10 |   16 |        3 | passes in front
  15 |             11 |   15 |        4 | passes in front
(12 rows)

See Also

Indices and tables