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.

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, 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)
pgr_dagShortestPath(Edges SQL, Combinations) -- Experimental on v3.2

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)

Combinations

pgr_dagShortestPath(Edges SQL, Combinations)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET

Example

Using a combinations table on a Directed Acyclic Graph.

SELECT * FROM pgr_dagShortestPath(
    'SELECT id, source, target, cost FROM edge_table',
    'SELECT * FROM ( VALUES (1, 6), (4, 12) ) AS t(source, target)'
);
 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 |    4 |   16 |    1 |        0
   6 |        2 |    9 |   15 |    1 |        1
   7 |        3 |   12 |   -1 |    0 |        2
(7 rows)

Parameters

Description of the parameters of the signatures

Parameter	Type	Default	Description
Edges SQL	TEXT		Edges query as described below.
Combinations SQL	TEXT		Combinations 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 Queries

Edges 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

Combinations query

Column	Type	Default	Description
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.

Where:

ANY-INTEGER

SMALLINT, INTEGER, BIGINT

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. Many to One Many to Many
end_vid	BIGINT	Identifier of the ending vertex. Returned when multiple ending vertices are in the query. One to Many Many to Many
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

• https://en.wikipedia.org/wiki/Topological_sorting

• The queries use the Sample Data network.

Indices and tables

• Index

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