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
(seq, path_seq, node, edge, cost, agg_cost)One to One¶
(seq, path_seq, node, edge, cost, agg_cost)- 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¶
(seq, path_seq, node, edge, cost, agg_cost)- 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¶
(seq, path_seq, node, edge, cost, agg_cost)- 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¶
(seq, path_seq, node, edge, cost, agg_cost)- 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¶
(seq, path_seq, node, edge, cost, agg_cost)- 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 as described below |
|
|
Combinations SQL as described below |
|
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 SQL¶
Column |
Type |
Default |
Description |
|---|---|---|---|
|
ANY-INTEGER |
Identifier of the edge. |
|
|
ANY-INTEGER |
Identifier of the first end point vertex of the edge. |
|
|
ANY-INTEGER |
Identifier of the second end point vertex of the edge. |
|
|
ANY-NUMERICAL |
Weight of the edge ( |
|
|
ANY-NUMERICAL |
-1 |
Weight of the edge (
|
Where:
- ANY-INTEGER:
SMALLINT,INTEGER,BIGINT- ANY-NUMERICAL:
SMALLINT,INTEGER,BIGINT,REAL,FLOAT
Combinations SQL¶
Parameter |
Type |
Description |
|---|---|---|
|
ANY-INTEGER |
Identifier of the departure vertex. |
|
ANY-INTEGER |
Identifier of the arrival vertex. |
Where:
- ANY-INTEGER:
SMALLINT,INTEGER,BIGINT
Resturn Columns¶
Returns set of (seq, path_seq [, start_vid] [, end_vid], node, edge, cost,
agg_cost)
Column |
Type |
Description |
|---|---|---|
|
|
Sequential value starting from 1. |
|
|
Relative position in the path. Has value 1 for the beginning of a path. |
|
|
Identifier of the starting vertex. Returned when multiple starting vetrices are in the query. |
|
|
Identifier of the ending vertex. Returned when multiple ending vertices are in the query. |
|
|
Identifier of the node in the path from |
|
|
Identifier of the edge used to go from |
|
|
Cost to traverse from |
|
|
Aggregate cost from |
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