pgr_withPointsKSP - Proposed

pgr_withPointsKSP — Yen’s algorithm for K shortest paths using Dijkstra.

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

Description

Modifies the graph to include the points defined in the Points SQL and using Yen algorithm, finds the \(K\) shortest paths.

Signatures

pgr_withPointsKSP(Edges SQL, Points SQL start_pid, end_pid, K
  [, directed] [, heap_paths] [, driving_side] [, details])
RETURNS SET OF (seq, path_id, path_seq, node, edge, cost, agg_cost)
Example:Get 2 paths from Point \(1\) to point \(2\) on a directed graph.
  • 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 the query.
  • No heap paths are returned.
SELECT * FROM pgr_withPointsKSP(
    'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
    'SELECT pid, edge_id, fraction, side from pointsOfInterest',
    -1, -2, 2);
 seq | path_id | path_seq | node | edge | cost | agg_cost
-----+---------+----------+------+------+------+----------
   1 |       1 |        1 |   -1 |    1 |  0.6 |        0
   2 |       1 |        2 |    6 |    4 |    1 |      0.6
   3 |       1 |        3 |    7 |    8 |    1 |      1.6
   4 |       1 |        4 |   11 |    9 |    1 |      2.6
   5 |       1 |        5 |   16 |   15 |  0.4 |      3.6
   6 |       1 |        6 |   -2 |   -1 |    0 |        4
   7 |       2 |        1 |   -1 |    1 |  0.6 |        0
   8 |       2 |        2 |    6 |    4 |    1 |      0.6
   9 |       2 |        3 |    7 |    8 |    1 |      1.6
  10 |       2 |        4 |   11 |   11 |    1 |      2.6
  11 |       2 |        5 |   12 |   13 |    1 |      3.6
  12 |       2 |        6 |   17 |   15 |  0.6 |      4.6
  13 |       2 |        7 |   -2 |   -1 |    0 |      5.2
(13 rows)

Parameters

Column Type Description
Edges SQL TEXT Edges SQL query as described.
Points SQL TEXT Points SQL query as described.
start vid ANY-INTEGER Identifier of the departure vertex.
end vid ANY-INTEGER Identifier of the departure vertex.
K ANY-INTEGER Number of required paths

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.

KSP Optional parameters

Column Type Default Description
heap_paths BOOLEAN false
  • When false Returns at most K paths
  • When true all the calculated paths while processing are returned.
  • Roughly, when the shortest path has N edges, the heap will contain about than N * K paths for small value of K and K > 5.

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

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.
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.

  • \(0\) for the last node of the path.
agg_cost FLOAT Aggregate cost from start vid to node.

Additional Examples

Left driving side

Get \(2\) paths using left side driving topology, from point \(1\) to point \(2\) with details.

SELECT * FROM pgr_withPointsKSP(
    'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
    'SELECT pid, edge_id, fraction, side from pointsOfInterest',
    -1, -2, 2,
    driving_side := 'l', details := true);
 seq | path_id | path_seq | node | edge | cost | agg_cost
-----+---------+----------+------+------+------+----------
   1 |       1 |        1 |   -1 |    1 |  0.6 |        0
   2 |       1 |        2 |    6 |    4 |  0.7 |      0.6
   3 |       1 |        3 |   -6 |    4 |  0.3 |      1.3
   4 |       1 |        4 |    7 |    8 |    1 |      1.6
   5 |       1 |        5 |   11 |   11 |    1 |      2.6
   6 |       1 |        6 |   12 |   13 |    1 |      3.6
   7 |       1 |        7 |   17 |   15 |  0.6 |      4.6
   8 |       1 |        8 |   -2 |   -1 |    0 |      5.2
   9 |       2 |        1 |   -1 |    1 |  0.6 |        0
  10 |       2 |        2 |    6 |    4 |  0.7 |      0.6
  11 |       2 |        3 |   -6 |    4 |  0.3 |      1.3
  12 |       2 |        4 |    7 |    8 |    1 |      1.6
  13 |       2 |        5 |   11 |    9 |    1 |      2.6
  14 |       2 |        6 |   16 |   15 |    1 |      3.6
  15 |       2 |        7 |   17 |   15 |  0.6 |      4.6
  16 |       2 |        8 |   -2 |   -1 |    0 |      5.2
(16 rows)

Right driving side

Get \(2\) paths using right side driving topology from, point \(1\) to point \(2\) with heap paths and details.

SELECT * FROM pgr_withPointsKSP(
    'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
    'SELECT pid, edge_id, fraction, side from pointsOfInterest',
    -1, -2, 2,
    heap_paths := true, driving_side := 'r', details := true);
 seq | path_id | path_seq | node | edge | cost | agg_cost
-----+---------+----------+------+------+------+----------
   1 |       1 |        1 |   -1 |    1 |  0.4 |        0
   2 |       1 |        2 |    5 |    1 |    1 |      0.4
   3 |       1 |        3 |    6 |    4 |  0.7 |      1.4
   4 |       1 |        4 |   -6 |    4 |  0.3 |      2.1
   5 |       1 |        5 |    7 |    8 |    1 |      2.4
   6 |       1 |        6 |   11 |    9 |    1 |      3.4
   7 |       1 |        7 |   16 |   15 |  0.4 |      4.4
   8 |       1 |        8 |   -2 |   -1 |    0 |      4.8
   9 |       2 |        1 |   -1 |    1 |  0.4 |        0
  10 |       2 |        2 |    5 |    1 |    1 |      0.4
  11 |       2 |        3 |    6 |    4 |  0.7 |      1.4
  12 |       2 |        4 |   -6 |    4 |  0.3 |      2.1
  13 |       2 |        5 |    7 |    8 |    1 |      2.4
  14 |       2 |        6 |   11 |   11 |    1 |      3.4
  15 |       2 |        7 |   12 |   13 |    1 |      4.4
  16 |       2 |        8 |   17 |   15 |    1 |      5.4
  17 |       2 |        9 |   16 |   15 |  0.4 |      6.4
  18 |       2 |       10 |   -2 |   -1 |    0 |      6.8
  19 |       3 |        1 |   -1 |    1 |  0.4 |        0
  20 |       3 |        2 |    5 |    1 |    1 |      0.4
  21 |       3 |        3 |    6 |    4 |  0.7 |      1.4
  22 |       3 |        4 |   -6 |    4 |  0.3 |      2.1
  23 |       3 |        5 |    7 |   10 |    1 |      2.4
  24 |       3 |        6 |    8 |   12 |  0.6 |      3.4
  25 |       3 |        7 |   -3 |   12 |  0.4 |        4
  26 |       3 |        8 |   12 |   13 |    1 |      4.4
  27 |       3 |        9 |   17 |   15 |    1 |      5.4
  28 |       3 |       10 |   16 |   15 |  0.4 |      6.4
  29 |       3 |       11 |   -2 |   -1 |    0 |      6.8
(29 rows)

The queries use the Sample Data network.