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 3.0.0
- New experimental function
Support
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, 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 | Default | 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)
|
|
reverse_cost | ANY-NUMERICAL |
-1 | Weight of the edge (target, source),
|
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. |
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_v to node . |
See Also¶
- https://en.wikipedia.org/wiki/Topological_sorting
- The queries use the Sample Data network.
Indices and tables