pgr_dagShortestPath - Experimental - pgRouting Manual (3.2)
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.
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 |
|
Edges query as described below. |
|
|
Combinations SQL |
|
Combinations query as described above. |
|
|
start_vid |
|
Identifier of the starting vertex of the path. |
|
|
start_vids |
|
Array of identifiers of starting vertices. |
|
|
end_vid |
|
Identifier of the ending vertex of the path. |
|
|
end_vids |
|
Array of identifiers of ending vertices. |
Inner Queries
Edges query
|
Column |
Type |
Default |
Description |
|---|---|---|---|
|
id |
|
Identifier of the edge. |
|
|
source |
|
Identifier of the first end point vertex of the edge. |
|
|
target |
|
Identifier of the second end point vertex of the edge. |
|
|
cost |
|
Weight of the edge (source, target)
|
|
|
reverse_cost |
|
-1 |
Weight of the edge (target, source) ,
|
Where:
- ANY-INTEGER :
-
SMALLINT, INTEGER, BIGINT
- ANY-NUMERICAL :
-
SMALLINT, INTEGER, BIGINT, REAL, FLOAT
Combinations query
|
Column |
Type |
Default |
Description |
|---|---|---|---|
|
source |
|
Identifier of the first end point vertex of the edge. |
|
|
target |
|
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 |
|
Sequential value starting from 1 . |
|
path_seq |
|
Relative position in the path. Has value 1 for the beginning of a path. |
|
start_vid |
|
Identifier of the starting vertex. Returned when multiple starting vetrices are in the query. |
|
end_vid |
|
Identifier of the ending vertex. Returned when multiple ending vertices are in the query. |
|
node |
|
Identifier of the node in the path from
|
|
edge |
|
Identifier of the edge used to go from
|
|
cost |
|
Cost to traverse from
|
|
agg_cost |
|
Aggregate cost from
|
See Also
-
The queries use the Sample Data network.
Indices and tables