pgr_withPoints - Proposed

Name

pgr_withPoints - Returns the shortest path in a graph with additional temporary 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: 2.2.0

Synopsis

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

Characteristics:

The main Characteristics are:

  • Process is done only on edges with positive costs.
  • Vertices of the graph are:
    • positive when it belongs to the edges_sql
    • negative when it belongs to the points_sql
  • 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: \(O(|start\_vids|\times(V \log V + E))\)

Signature Summary

pgr_withPoints(edges_sql, points_sql, start_vid, end_vid)
pgr_withPoints(edges_sql, points_sql, start_vid, end_vid, directed, driving_side, details)
pgr_withPoints(edges_sql, points_sql, start_vid, end_vids, directed, driving_side, details)
pgr_withPoints(edges_sql, points_sql, start_vids, end_vid, directed, driving_side, details)
pgr_withPoints(edges_sql, points_sql, start_vids, end_vids, directed, driving_side, details)
RETURNS SET OF (seq, path_seq, [start_vid,] [end_vid,] node, edge, cost, agg_cost)

Signatures

Minimal Use

The minimal signature:
  • Is for a directed graph.
  • The driving side is set as b both. So arriving/departing to/from the point(s) can be in any direction.
  • No details are given about distance of other points of points_sql query.
pgr_withPoints(edges_sql, points_sql, start_vid, end_vid)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
Example:From point 1 to point 3
SELECT * FROM pgr_withPoints(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
    'SELECT pid, edge_id, fraction, side from pointsOfInterest',
    -1, -3);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |   -1 |    1 |  0.6 |        0
   2 |        2 |    2 |    4 |    1 |      0.6
   3 |        3 |    5 |   10 |    1 |      1.6
   4 |        4 |   10 |   12 |  0.6 |      2.6
   5 |        5 |   -3 |   -1 |    0 |      3.2
(5 rows)

One to One

pgr_withPoints(edges_sql, points_sql, start_vid, end_vid,
    directed:=true, driving_side:='b', details:=false)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
Example:From point 1 to vertex 3
SELECT * FROM pgr_withPoints(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
    'SELECT pid, edge_id, fraction, side from pointsOfInterest',
    -1, 3,
    details := true);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |   -1 |    1 |  0.6 |        0
   2 |        2 |    2 |    4 |  0.7 |      0.6
   3 |        3 |   -6 |    4 |  0.3 |      1.3
   4 |        4 |    5 |    8 |    1 |      1.6
   5 |        5 |    6 |    9 |    1 |      2.6
   6 |        6 |    9 |   16 |    1 |      3.6
   7 |        7 |    4 |    3 |    1 |      4.6
   8 |        8 |    3 |   -1 |    0 |      5.6
(8 rows)

One to Many

pgr_withPoints(edges_sql, points_sql, start_vid, end_vids,
    directed:=true, driving_side:='b', details:=false)
RETURNS SET OF (seq, path_seq, end_vid, node, edge, cost, agg_cost)
Example:From point 1 to point 3 and vertex 5
SELECT * FROM pgr_withPoints(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
    'SELECT pid, edge_id, fraction, side from pointsOfInterest',
    -1, ARRAY[-3,5]);
 seq | path_seq | end_pid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
   1 |        1 |      -3 |   -1 |    1 |  0.6 |        0
   2 |        2 |      -3 |    2 |    4 |    1 |      0.6
   3 |        3 |      -3 |    5 |   10 |    1 |      1.6
   4 |        4 |      -3 |   10 |   12 |  0.6 |      2.6
   5 |        5 |      -3 |   -3 |   -1 |    0 |      3.2
   6 |        1 |       5 |   -1 |    1 |  0.6 |        0
   7 |        2 |       5 |    2 |    4 |    1 |      0.6
   8 |        3 |       5 |    5 |   -1 |    0 |      1.6
(8 rows)

Many to One

pgr_withPoints(edges_sql, points_sql, start_vids, end_vid,
    directed:=true, driving_side:='b', details:=false)
RETURNS SET OF (seq, path_seq, start_vid, node, edge, cost, agg_cost)
Example:From point 1 and vertex 2 to point 3
SELECT * FROM pgr_withPoints(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
    'SELECT pid, edge_id, fraction, side from pointsOfInterest',
    ARRAY[-1,2], -3);
 seq | path_seq | start_pid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
   1 |        1 |        -1 |   -1 |    1 |  0.6 |        0
   2 |        2 |        -1 |    2 |    4 |    1 |      0.6
   3 |        3 |        -1 |    5 |   10 |    1 |      1.6
   4 |        4 |        -1 |   10 |   12 |  0.6 |      2.6
   5 |        5 |        -1 |   -3 |   -1 |    0 |      3.2
   6 |        1 |         2 |    2 |    4 |    1 |        0
   7 |        2 |         2 |    5 |   10 |    1 |        1
   8 |        3 |         2 |   10 |   12 |  0.6 |        2
   9 |        4 |         2 |   -3 |   -1 |    0 |      2.6
(9 rows)

Many to Many

pgr_withPoints(edges_sql, points_sql, start_vids, end_vids,
    directed:=true, driving_side:='b', details:=false)
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
Example:From point 1 and vertex 2 to point 3 and vertex 7
SELECT * FROM pgr_withPoints(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
    'SELECT pid, edge_id, fraction, side from pointsOfInterest',
    ARRAY[-1,2], ARRAY[-3,7]);
 seq | path_seq | start_pid | end_pid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |        -1 |      -3 |   -1 |    1 |  0.6 |        0
   2 |        2 |        -1 |      -3 |    2 |    4 |    1 |      0.6
   3 |        3 |        -1 |      -3 |    5 |   10 |    1 |      1.6
   4 |        4 |        -1 |      -3 |   10 |   12 |  0.6 |      2.6
   5 |        5 |        -1 |      -3 |   -3 |   -1 |    0 |      3.2
   6 |        1 |        -1 |       7 |   -1 |    1 |  0.6 |        0
   7 |        2 |        -1 |       7 |    2 |    4 |    1 |      0.6
   8 |        3 |        -1 |       7 |    5 |    7 |    1 |      1.6
   9 |        4 |        -1 |       7 |    8 |    6 |    1 |      2.6
  10 |        5 |        -1 |       7 |    7 |   -1 |    0 |      3.6
  11 |        1 |         2 |      -3 |    2 |    4 |    1 |        0
  12 |        2 |         2 |      -3 |    5 |   10 |    1 |        1
  13 |        3 |         2 |      -3 |   10 |   12 |  0.6 |        2
  14 |        4 |         2 |      -3 |   -3 |   -1 |    0 |      2.6
  15 |        1 |         2 |       7 |    2 |    4 |    1 |        0
  16 |        2 |         2 |       7 |    5 |    7 |    1 |        1
  17 |        3 |         2 |       7 |    8 |    6 |    1 |        2
  18 |        4 |         2 |       7 |    7 |   -1 |    0 |        3
(18 rows)

Description of the Signatures

edges_sql:an SQL query, which should return a set of rows with the following columns:
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)

  • When negative: edge (source, target) does not exist, therefore it’s not part of the graph.
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

Description of the Points SQL query

points_sql:an SQL query, which should return a set of rows with the following columns:
Column Type Description
pid ANY-INTEGER

(optional) Identifier of the point.

  • If column present, it can not be NULL.
  • If column not present, a sequential identifier 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

(optional) Value in [‘b’, ‘r’, ‘l’, NULL] indicating if the point is:

  • In the right, left of the edge or
  • If it doesn’t matter with ‘b’ or NULL.
  • If column not present ‘b’ is considered.

Where:

ANY-INTEGER:smallint, int, bigint
ANY-NUMERICAL:smallint, int, bigint, real, float

Description of the parameters of the signatures

Parameter Type Description
edges_sql TEXT Edges SQL query as described above.
points_sql TEXT Points SQL query as described above.
start_vid ANY-INTEGER Starting vertex identifier. When negative: is a point’s pid.
end_vid ANY-INTEGER Ending vertex identifier. When negative: is a point’s pid.
start_vids ARRAY[ANY-INTEGER] Array of identifiers of starting vertices. When negative: is a point’s pid.
end_vids ARRAY[ANY-INTEGER] Array of identifiers of ending vertices. When negative: is a point’s pid.
directed BOOLEAN (optional). When false the graph is considered as Undirected. Default is true which considers the graph as Directed.
driving_side CHAR
(optional) Value in [‘b’, ‘r’, ‘l’, NULL] indicating if the driving side is:
  • In the right or left or
  • If it doesn’t matter with ‘b’ or NULL.
  • If column not present ‘b’ is considered.
details BOOLEAN (optional). When true the results will include the points in points_sql that are in the path. Default is false which ignores other points of the points_sql.

Description of the return values

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

Column Type Description
seq INTEGER Row sequence.
path_seq INTEGER Path sequence that indicates the relative position on the path.
start_vid BIGINT Identifier of the starting vertex. When negative: is a point’s pid.
end_vid BIGINT Identifier of the ending vertex. When negative: is a point’s pid.
node BIGINT
Identifier of the node:
  • A positive value indicates the node is a vertex of edges_sql.
  • A negative value indicates the node is a point of points_sql.
edge BIGINT
Identifier of the edge used to go from node to the next node in the path sequence.
  • -1 for the last row in the path sequence.
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_pid to node.
  • 0 for the first row in the path sequence.

Examples

Example:Which path (if any) passes in front of point 6 or vertex 6 with right side driving topology.
SELECT ('(' || start_pid || ' => ' || end_pid ||') 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_withPoints(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
        'SELECT pid, edge_id, fraction, side from pointsOfInterest',
        ARRAY[1,-1], ARRAY[-2,-3,-6,3,6],
        driving_side := 'r',
        details := true)
    WHERE node IN (-6,6);
         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 => -2) at 4th step: |  passes in front of | Point  |  6
 (-1 => -2) at 6th step: |  passes in front of | Vertex |  6
 (-1 => 3) at 4th step:  |  passes in front of | Point  |  6
 (-1 => 3) at 6th step:  |  passes in front of | Vertex |  6
 (-1 => 6) at 4th step:  |  passes in front of | Point  |  6
 (-1 => 6) at 6th step:  |  visits             | Vertex |  6
 (1 => -6) at 3th step:  |  visits             | Point  |  6
 (1 => -3) at 3th step:  |  passes in front of | Point  |  6
 (1 => -2) at 3th step:  |  passes in front of | Point  |  6
 (1 => -2) at 5th step:  |  passes in front of | Vertex |  6
 (1 => 3) at 3th step:   |  passes in front of | Point  |  6
 (1 => 3) at 5th step:   |  passes in front of | Vertex |  6
 (1 => 6) at 3th step:   |  passes in front of | Point  |  6
 (1 => 6) at 5th step:   |  visits             | Vertex |  6
(16 rows)

Example:Which path (if any) passes in front of point 6 or vertex 6 with left side driving topology.
SELECT ('(' || start_pid || ' => ' || end_pid ||') 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_withPoints(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
        'SELECT pid, edge_id, fraction, side from pointsOfInterest',
        ARRAY[1,-1], ARRAY[-2,-3,-6,3,6],
        driving_side := 'l',
        details := true)
    WHERE node IN (-6,6);
         path_at         |       status        |  is_a  | id
-------------------------+---------------------+--------+----
 (-1 => -6) at 3th step: |  visits             | Point  |  6
 (-1 => -3) at 3th step: |  passes in front of | Point  |  6
 (-1 => -2) at 3th step: |  passes in front of | Point  |  6
 (-1 => -2) at 5th step: |  passes in front of | Vertex |  6
 (-1 => 3) at 3th step:  |  passes in front of | Point  |  6
 (-1 => 3) at 5th step:  |  passes in front of | Vertex |  6
 (-1 => 6) at 3th step:  |  passes in front of | Point  |  6
 (-1 => 6) at 5th step:  |  visits             | Vertex |  6
 (1 => -6) at 4th step:  |  visits             | Point  |  6
 (1 => -3) at 4th step:  |  passes in front of | Point  |  6
 (1 => -2) at 4th step:  |  passes in front of | Point  |  6
 (1 => -2) at 6th step:  |  passes in front of | Vertex |  6
 (1 => 3) at 4th step:   |  passes in front of | Point  |  6
 (1 => 3) at 6th step:   |  passes in front of | Vertex |  6
 (1 => 6) at 4th step:   |  passes in front of | Point  |  6
 (1 => 6) at 6th step:   |  visits             | Vertex |  6
(16 rows)

Example:Many to many example with a twist: on undirected graph and showing details.
SELECT * FROM pgr_withPoints(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
    'SELECT pid, edge_id, fraction, side from pointsOfInterest',
    ARRAY[-1,2], ARRAY[-3,7],
    directed := false,
    details := true);
 seq | path_seq | start_pid | end_pid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |        -1 |      -3 |   -1 |    1 |  0.6 |        0
   2 |        2 |        -1 |      -3 |    2 |    4 |  0.7 |      0.6
   3 |        3 |        -1 |      -3 |   -6 |    4 |  0.3 |      1.3
   4 |        4 |        -1 |      -3 |    5 |   10 |    1 |      1.6
   5 |        5 |        -1 |      -3 |   10 |   12 |  0.6 |      2.6
   6 |        6 |        -1 |      -3 |   -3 |   -1 |    0 |      3.2
   7 |        1 |        -1 |       7 |   -1 |    1 |  0.6 |        0
   8 |        2 |        -1 |       7 |    2 |    4 |  0.7 |      0.6
   9 |        3 |        -1 |       7 |   -6 |    4 |  0.3 |      1.3
  10 |        4 |        -1 |       7 |    5 |    7 |    1 |      1.6
  11 |        5 |        -1 |       7 |    8 |    6 |  0.7 |      2.6
  12 |        6 |        -1 |       7 |   -4 |    6 |  0.3 |      3.3
  13 |        7 |        -1 |       7 |    7 |   -1 |    0 |      3.6
  14 |        1 |         2 |      -3 |    2 |    4 |  0.7 |        0
  15 |        2 |         2 |      -3 |   -6 |    4 |  0.3 |      0.7
  16 |        3 |         2 |      -3 |    5 |   10 |    1 |        1
  17 |        4 |         2 |      -3 |   10 |   12 |  0.6 |        2
  18 |        5 |         2 |      -3 |   -3 |   -1 |    0 |      2.6
  19 |        1 |         2 |       7 |    2 |    4 |  0.7 |        0
  20 |        2 |         2 |       7 |   -6 |    4 |  0.3 |      0.7
  21 |        3 |         2 |       7 |    5 |    7 |    1 |        1
  22 |        4 |         2 |       7 |    8 |    6 |  0.7 |        2
  23 |        5 |         2 |       7 |   -4 |    6 |  0.3 |      2.7
  24 |        6 |         2 |       7 |    7 |   -1 |    0 |        3
(24 rows)

The queries use the Sample Data network.

History

  • Proposed in version 2.2