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pgr_dagShortestPath - Experimental - pgRouting Manual (3.0)

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

Supported versions: current( 3.0 )

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	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. 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` .

pgr_dagShortestPath - Experimental - pgRouting Manual (3.0)