pgr_dagShortestPath - Experimental

pgr_dagShortestPath — Returns the shortest path(s) 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 3.0.0
    • New experimental function

Support

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, from_vid,  to_vid)
pgr_dagShortestPath(edges_sql, from_vid,  to_vids)
pgr_dagShortestPath(edges_sql, from_vids, to_vid)
pgr_dagShortestPath(edges_sql, from_vids, to_vids)

RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET

One to One

pgr_dagShortestPath(edges_sql, from_vid,  to_vid)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET
Example:From vertex \(1\) to vertex \(6\) 
SELECT * FROM pgr_dagShortestPath(
    'SELECT id, source, target, cost FROM edge_table',
    1, 6
);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |    1 |    1 |    1 |        0
   2 |        2 |    2 |    4 |    1 |        1
   3 |        3 |    5 |    8 |    1 |        2
   4 |        4 |    6 |   -1 |    0 |        3
(4 rows)

One to Many

pgr_dagShortestPath(edges_sql, from_vid,  to_vids)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET
Example:From vertex \(1\) to vertices \(\{ 5, 6\}\) 
SELECT * FROM pgr_dagShortestPath(
    'SELECT id, source, target, cost FROM edge_table',
    1, ARRAY[5,6]
);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |    1 |    1 |    1 |        0
   2 |        2 |    2 |    4 |    1 |        1
   3 |        3 |    5 |   -1 |    0 |        2
   4 |        1 |    1 |    1 |    1 |        0
   5 |        2 |    2 |    4 |    1 |        1
   6 |        3 |    5 |    8 |    1 |        2
   7 |        4 |    6 |   -1 |    0 |        3
(7 rows)

Many to One

pgr_dagShortestPath(edges_sql, from_vids, to_vid)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET
Example:From vertices \(\{1, 3\}\) to vertex \(6\) 
SELECT * FROM pgr_dagShortestPath(
    'SELECT id, source, target, cost FROM edge_table',
    ARRAY[1,3], 6
);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |    1 |    1 |    1 |        0
   2 |        2 |    2 |    4 |    1 |        1
   3 |        3 |    5 |    8 |    1 |        2
   4 |        4 |    6 |   -1 |    0 |        3
   5 |        1 |    3 |    5 |    1 |        0
   6 |        2 |    6 |   -1 |    0 |        1
(6 rows)

Many to Many

pgr_dagShortestPath(edges_sql, from_vids, to_vids)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET
Example:From vertices \(\{1, 4\}\) to vertices \(\{12, 6\}\) 
SELECT * FROM pgr_dagShortestPath(
    'SELECT id, source, target, cost FROM edge_table',
    ARRAY[1, 4],ARRAY[12,6]
);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |    1 |    1 |    1 |        0
   2 |        2 |    2 |    4 |    1 |        1
   3 |        3 |    5 |    8 |    1 |        2
   4 |        4 |    6 |   -1 |    0 |        3
   5 |        1 |    1 |    1 |    1 |        0
   6 |        2 |    2 |    4 |    1 |        1
   7 |        3 |    5 |   10 |    1 |        2
   8 |        4 |   10 |   12 |    1 |        3
   9 |        5 |   11 |   13 |    1 |        4
  10 |        6 |   12 |   -1 |    0 |        5
  11 |        1 |    4 |   16 |    1 |        0
  12 |        2 |    9 |   15 |    1 |        1
  13 |        3 |   12 |   -1 |    0 |        2
(13 rows)

Parameters

Description of the parameters of the signatures

Parameter Type Default Description
edges_sql TEXT   SQL query as described above.
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 Query

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

Results Columns

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

Column Type Description
seq INT Sequential value starting from 1.
path_seq INT 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_v to node.

See Also

Indices and tables