pgr_dagShortestPath - Experimental

pgr_dagShortestPath — Returns the shortest path for weighted directed acyclic graphs(DAG). In particular, the DAG shortest paths algorithm implemented by Boost.Graph.

_images/boost-inside.jpeg

Boost Graph Inside

Warning

Possible server crash

  • These functions might create a server crash

Warning

Experimental functions

  • They are not officially of the current release.

  • They likely will not be officially be part of the next release:

    • The functions might not make use of ANY-INTEGER and ANY-NUMERICAL

    • Name might change.

    • Signature might change.

    • Functionality might change.

    • pgTap tests might be missing.

    • Might need c/c++ coding.

    • May lack documentation.

    • Documentation if any might need to be rewritten.

    • Documentation examples might need to be automatically generated.

    • Might need a lot of feedback from the comunity.

    • Might depend on a proposed function of pgRouting

    • Might depend on a deprecated function of pgRouting

Availability

  • Version 3.2.0

    • New experimental function:

      • pgr_dagShortestPath(Combinations)

  • Version 3.0.0

    • New experimental function

Description

Shortest Path for Directed Acyclic Graph(DAG) is a graph search algorithm that solves the shortest path problem for weighted directed acyclic graph, producing a shortest path from a starting vertex (start_vid) to an ending vertex (end_vid).

This implementation can only be used with a directed graph with no cycles i.e. directed acyclic graph.

The algorithm relies on topological sorting the dag to impose a linear ordering on the vertices, and thus is more efficient for DAG’s than either the Dijkstra or Bellman-Ford algorithm.

The main characteristics are:

  • Process is valid for weighted directed acyclic graphs only. otherwise it will throw warnings.

  • 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 \(\infty\)

  • 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: \(O(| start\_vids | * (V + E))\)

Signatures

Summary

pgr_dagShortestPath(Edges SQL, start vid, end vid)
pgr_dagShortestPath(Edges SQL, start vid, end vids)
pgr_dagShortestPath(Edges SQL, start vids, end vid)
pgr_dagShortestPath(Edges SQL, start vids, end vids)
pgr_dagShortestPath(Edges SQL, Combinations SQL)
Returns set of (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET

One to One

pgr_dagShortestPath(Edges SQL, start vid, end vid)
Returns set of (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET
Example:

From vertex \(5\) to vertex \(11\) on a directed graph

SELECT * FROM pgr_dagShortestPath(
  'SELECT id, source, target, cost FROM edges',
  5, 11);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |    5 |    1 |    1 |        0
   2 |        2 |    6 |    4 |    1 |        1
   3 |        3 |    7 |    8 |    1 |        2
   4 |        4 |   11 |   -1 |    0 |        3
(4 rows)

One to Many

pgr_dagShortestPath(Edges SQL, start vid, end vids)
Returns set of (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET
Example:

From vertex \(5\) to vertices \(\{7, 11\}\)

SELECT * FROM pgr_dagShortestPath(
  'SELECT id, source, target, cost FROM edges',
  5, ARRAY[7, 11]);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |    5 |    1 |    1 |        0
   2 |        2 |    6 |    4 |    1 |        1
   3 |        3 |    7 |   -1 |    0 |        2
   4 |        1 |    5 |    1 |    1 |        0
   5 |        2 |    6 |    4 |    1 |        1
   6 |        3 |    7 |    8 |    1 |        2
   7 |        4 |   11 |   -1 |    0 |        3
(7 rows)

Many to One

pgr_dagShortestPath(Edges SQL, start vids, end vid)
Returns set of (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET
Example:

From vertices \(\{5, 10\}\) to vertex \(11\)

SELECT * FROM pgr_dagShortestPath(
  'SELECT id, source, target, cost FROM edges',
  ARRAY[5, 10], 11);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |    5 |    1 |    1 |        0
   2 |        2 |    6 |    4 |    1 |        1
   3 |        3 |    7 |    8 |    1 |        2
   4 |        4 |   11 |   -1 |    0 |        3
   5 |        1 |   10 |    5 |    1 |        0
   6 |        2 |   11 |   -1 |    0 |        1
(6 rows)

Many to Many

pgr_dagShortestPath(Edges SQL, start vids, end vids)
Returns set of (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET
Example:

From vertices \(\{5, 15\}\) to vertices \(\{11, 17\}\) on an undirected graph

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

Combinations

pgr_dagShortestPath(Edges SQL, Combinations SQL)
Returns set of (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET
Example:

Using a combinations table on an undirected graph

The combinations table:

SELECT source, target FROM combinations;
 source | target
--------+--------
      5 |      6
      5 |     10
      6 |      5
      6 |     15
      6 |     14
(5 rows)

The query:

SELECT * FROM pgr_dagShortestPath(
  'SELECT id, source, target, cost FROM edges',
  'SELECT source, target FROM combinations');
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |    5 |    1 |    1 |        0
   2 |        2 |    6 |   -1 |    0 |        1
(2 rows)

Parameters

Column

Type

Description

Edges SQL

TEXT

Edges SQL as described below

Combinations SQL

TEXT

Combinations SQL as described below

start vid

BIGINT

Identifier of the starting vertex of the path.

start vids

ARRAY[BIGINT]

Array of identifiers of starting vertices.

end vid

BIGINT

Identifier of the ending vertex of the path.

end vids

ARRAY[BIGINT]

Array of identifiers of ending vertices.

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

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

Return columns

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

Column

Type

Description

seq

INTEGER

Sequential value starting from 1.

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. Returned when multiple starting vetrices are in the query.

end_vid

BIGINT

Identifier of the ending vertex. Returned when multiple ending vertices are in the query.

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

Example 1:

Demonstration of repeated values are ignored, and result is sorted.

SELECT * FROM pgr_dagShortestPath(
  'SELECT id, source, target, cost FROM edges',
  ARRAY[5, 10, 5, 10, 10, 5], ARRAY[11, 17, 17, 11]);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |    5 |    1 |    1 |        0
   2 |        2 |    6 |    4 |    1 |        1
   3 |        3 |    7 |    8 |    1 |        2
   4 |        4 |   11 |   -1 |    0 |        3
   5 |        1 |    5 |    1 |    1 |        0
   6 |        2 |    6 |    4 |    1 |        1
   7 |        3 |    7 |    8 |    1 |        2
   8 |        4 |   11 |    9 |    1 |        3
   9 |        5 |   16 |   15 |    1 |        4
  10 |        6 |   17 |   -1 |    0 |        5
  11 |        1 |   10 |    5 |    1 |        0
  12 |        2 |   11 |   -1 |    0 |        1
  13 |        1 |   10 |    5 |    1 |        0
  14 |        2 |   11 |    9 |    1 |        1
  15 |        3 |   16 |   15 |    1 |        2
  16 |        4 |   17 |   -1 |    0 |        3
(16 rows)
Example 2:

Making start_vids the same as end_vids

SELECT * FROM pgr_dagShortestPath(
  'SELECT id, source, target, cost FROM edges',
  ARRAY[5, 10, 11], ARRAY[5, 10, 11]);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |    5 |    1 |    1 |        0
   2 |        2 |    6 |    4 |    1 |        1
   3 |        3 |    7 |    8 |    1 |        2
   4 |        4 |   11 |   -1 |    0 |        3
   5 |        1 |   10 |    5 |    1 |        0
   6 |        2 |   11 |   -1 |    0 |        1
(6 rows)
Example 3:

Manually assigned vertex combinations.

SELECT * FROM pgr_dagShortestPath(
  'SELECT id, source, target, cost FROM edges',
  'SELECT * FROM (VALUES (6, 10), (6, 7), (12, 10)) AS combinations (source, target)');
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |    6 |    4 |    1 |        0
   2 |        2 |    7 |   -1 |    0 |        1
(2 rows)

See Also

Indices and tables