pgr_aStar¶

pgr_aStar — Returns the shortest path using A* algorithm.

Boost Graph Inside

Availability

Official on v3.0.0
Proposed on v2.4.0:
- pgr_astar(One to Many)
- pgr_astar(Many to One)
- pgr_astar(Many to Many)
Signature change on v2.3.0:
- pgr_astar(One to One)
New on v2.0.0:
- pgr_astar(One to One)

Description¶

The main characteristics are:

Default kind of graph is directed when
- directed flag is missing.
- directed flag is set to true
Unless specified otherwise, ordering is:
- first by start_vid (if exists)
- then by end_vid
Values are returned when there is a path
Let \(v\) and \(u\) be nodes on the graph:
- If there is no path from \(v\) to \(u\):
  - no corresponding row is returned
  - agg_cost from \(v\) to \(u\) is \(\infty\)
- There is no path when \(v = u\) therefore
  - no corresponding row is returned
  - agg_cost from v to u is \(0\)
Edges with negative costs are not included in the graph.
When (x,y) coordinates for the same vertex identifier differ:
- A random selection of the vertex’s (x,y) coordinates is used.
Running time: \(O((E + V) * \log V)\)

The results are equivalent to the union of the results of the pgr_aStar( One to One ) on the:
- pgr_aStar( One to Many )
- pgr_aStar( Many to One )
- pgr_aStar( Many to Many )
start_vid and end_vid in the result is used to distinguish to which path it belongs.

Signatures¶

Summary

pgr_aStar(edges_sql, from_vid,  to_vid  [, directed] [, heuristic] [, factor] [, epsilon])
pgr_aStar(edges_sql, from_vid,  to_vids [, directed] [, heuristic] [, factor] [, epsilon])
pgr_aStar(edges_sql, from_vids, to_vid  [, directed] [, heuristic] [, factor] [, epsilon])
pgr_aStar(edges_sql, from_vids, to_vids [, directed] [, heuristic] [, factor] [, epsilon])

RETURNS SET OF (seq, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)
OR EMPTY SET

Optional parameters are named parameters and have a default value.

Using defaults

pgr_aStar(edges_sql, from_vid, to_vid)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET

Example:	From vertex \(2\) to vertex \(12\) on a directed graph

SELECT * FROM pgr_astar(
    'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
    2, 12);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |    2 |    4 |    1 |        0
   2 |        2 |    5 |   10 |    1 |        1
   3 |        3 |   10 |   12 |    1 |        2
   4 |        4 |   11 |   13 |    1 |        3
   5 |        5 |   12 |   -1 |    0 |        4
(5 rows)

One to One¶

pgr_aStar(edges_sql, from_vid,  to_vid  [, directed] [, heuristic] [, factor] [, epsilon])

RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET

Example:	From vertex \(2\) to vertex \(12\) on an undirected graph using heuristic \(2\)

SELECT * FROM pgr_astar(
    'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
    2, 12,
    directed := false, heuristic := 2);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |    2 |    4 |    1 |        0
   2 |        2 |    5 |    8 |    1 |        1
   3 |        3 |    6 |   11 |    1 |        2
   4 |        4 |   11 |   13 |    1 |        3
   5 |        5 |   12 |   -1 |    0 |        4
(5 rows)

One to many¶

pgr_aStar(edges_sql, from_vid,  to_vids [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (seq, path_seq, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET

Example:	From vertex \(2\) to vertices \(\{3, 12\}\) on a directed graph using heuristic \(2\)

SELECT * FROM pgr_astar(
    'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
    2, ARRAY[3, 12], heuristic := 2);
 seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
   1 |        1 |       3 |    2 |    4 |    1 |        0
   2 |        2 |       3 |    5 |    8 |    1 |        1
   3 |        3 |       3 |    6 |    9 |    1 |        2
   4 |        4 |       3 |    9 |   16 |    1 |        3
   5 |        5 |       3 |    4 |    3 |    1 |        4
   6 |        6 |       3 |    3 |   -1 |    0 |        5
   7 |        1 |      12 |    2 |    4 |    1 |        0
   8 |        2 |      12 |    5 |    8 |    1 |        1
   9 |        3 |      12 |    6 |   11 |    1 |        2
  10 |        4 |      12 |   11 |   13 |    1 |        3
  11 |        5 |      12 |   12 |   -1 |    0 |        4
(11 rows)

Many to One¶

pgr_aStar(edges_sql, from_vids, to_vid  [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (seq, path_seq, start_vid, node, edge, cost, agg_cost)
OR EMPTY SET

Example:	From vertices \(\{7, 2\}\) to vertex \(12\) on a directed graph using heuristic \(0\)

SELECT * FROM pgr_astar(
    'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
    ARRAY[7, 2], 12, heuristic := 0);
 seq | path_seq | start_vid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
   1 |        1 |         2 |    2 |    4 |    1 |        0
   2 |        2 |         2 |    5 |   10 |    1 |        1
   3 |        3 |         2 |   10 |   12 |    1 |        2
   4 |        4 |         2 |   11 |   13 |    1 |        3
   5 |        5 |         2 |   12 |   -1 |    0 |        4
   6 |        1 |         7 |    7 |    6 |    1 |        0
   7 |        2 |         7 |    8 |    7 |    1 |        1
   8 |        3 |         7 |    5 |   10 |    1 |        2
   9 |        4 |         7 |   10 |   12 |    1 |        3
  10 |        5 |         7 |   11 |   13 |    1 |        4
  11 |        6 |         7 |   12 |   -1 |    0 |        5
(11 rows)

Many to Many¶

pgr_aStar(edges_sql, from_vids, to_vids [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET

Example:	From vertices \(\{7, 2\}\) to vertices \(\{3, 12\}\) on a directed graph using heuristic \(2\)

SELECT * FROM pgr_astar(
    'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
    ARRAY[7, 2], ARRAY[3, 12], heuristic := 2);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
|        1 |         2 |       3 |    2 |    4 |    1 |        0
|        2 |         2 |       3 |    5 |    8 |    1 |        1
|        3 |         2 |       3 |    6 |    9 |    1 |        2
|        4 |         2 |       3 |    9 |   16 |    1 |        3
|        5 |         2 |       3 |    4 |    3 |    1 |        4
|        6 |         2 |       3 |    3 |   -1 |    0 |        5
|        1 |         7 |       3 |    7 |    6 |    1 |        0
|        2 |         7 |       3 |    8 |    7 |    1 |        1
|        3 |         7 |       3 |    5 |    8 |    1 |        2
|        4 |         7 |       3 |    6 |    9 |    1 |        3
|        5 |         7 |       3 |    9 |   16 |    1 |        4
|        6 |         7 |       3 |    4 |    3 |    1 |        5
|        7 |         7 |       3 |    3 |   -1 |    0 |        6
|        1 |         2 |      12 |    2 |    4 |    1 |        0
|        2 |         2 |      12 |    5 |   10 |    1 |        1
|        3 |         2 |      12 |   10 |   12 |    1 |        2
|        4 |         2 |      12 |   11 |   13 |    1 |        3
|        5 |         2 |      12 |   12 |   -1 |    0 |        4
|        1 |         7 |      12 |    7 |    6 |    1 |        0
|        2 |         7 |      12 |    8 |    7 |    1 |        1
|        3 |         7 |      12 |    5 |   10 |    1 |        2
|        4 |         7 |      12 |   10 |   12 |    1 |        3
|        5 |         7 |      12 |   11 |   13 |    1 |        4
|        6 |         7 |      12 |   12 |   -1 |    0 |        5
(24 rows)

Parameters¶

Parameter	Type	Description
edges_sql	`TEXT`	edges_sql inner query.
from_vid	`ANY-INTEGER`	Starting vertex identifier. Parameter in: One to One One to Many
from_vids	`ARRAY[ANY-INTEGER]`	Array of starting vertices identifiers. Parameter in: Many to One Many to Many
to_vid	`ANY-INTEGER`	Ending vertex identifier. Parameter in: One to One Many to One
to_vids	`ARRAY[ANY-INTEGER]`	Array of ending vertices identifiers. Parameter in: One to Many Many to Many

Optional Parameters¶

Parameter	Type	Default	Description
directed	`BOOLEAN`	`true`	When `true` the graph is considered as Directed. When `false` the graph is considered as Undirected.
heuristic	`INTEGER`	`5`	Heuristic number. Current valid values 0~5. Default `5` 0: h(v) = 0 (Use this value to compare with pgr_dijkstra) 1: h(v) abs(max(dx, dy)) 2: h(v) abs(min(dx, dy)) 3: h(v) = dx * dx + dy * dy 4: h(v) = sqrt(dx * dx + dy * dy) 5: h(v) = abs(dx) + abs(dy)
factor	`FLOAT`	`1`	For units manipulation. \(factor > 0\). See Factor
epsilon	`FLOAT`	`1`	For less restricted results. \(epsilon >= 1\).

Inner query¶

edges_sql¶

edges_sql:	an SQL query, which should return a set of rows with the following columns:

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.
x1	`ANY-NUMERICAL`		X coordinate of source vertex.
y1	`ANY-NUMERICAL`		Y coordinate of source vertex.
x2	`ANY-NUMERICAL`		X coordinate of target vertex.
y2	`ANY-NUMERICAL`		Y coordinate of target vertex.

Where:

ANY-INTEGER:	SMALLINT, INTEGER, BIGINT
ANY-NUMERICAL:	SMALLINT, INTEGER, BIGINT, REAL, FLOAT

Result 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`.