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)
- New experimental function:
- 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 \(\infty\)
- When the starting vertex and ending vertex are the same, there is no path.
- 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, start vid, end vid) pgr_dagShortestPath(Edges SQL, start vid, end vids) pgr_dagShortestPath(Edges SQL, start vids, end vid) pgr_dagShortestPath(Edges SQL, start vids, end vids) pgr_dagShortestPath(Edges SQL, Combinations SQL) RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost) OR EMPTY SET
One to One¶
pgr_dagShortestPath(Edges SQL, start vid, end vid) RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost) OR EMPTY SET
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¶
pgr_dagShortestPath(Edges SQL, start vid, end vids) RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost) OR EMPTY SET
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¶
pgr_dagShortestPath(Edges SQL, start vids, end vid) RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost) OR EMPTY SET
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¶
pgr_dagShortestPath(Edges SQL, start vids, end vids) RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost) OR EMPTY SET
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¶
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 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 | TEXT |
Edges SQL as described below |
Combinations SQL | TEXT |
Combinations SQL as described below |
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 SQL¶
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 ) |
|
reverse_cost |
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 |
---|---|---|
source |
ANY-INTEGER | Identifier of the departure vertex. |
target |
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 |
---|---|---|
seq |
INTEGER |
Sequential value starting from 1. |
path_seq |
INTEGER |
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_vid to node . |
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