pgr_bdAstar¶

Name¶

pgr_bdAstar — Returns the shortest path using A* algorithm.

Boost Graph Inside

Availability:

pgr_bdAstar(one to one) 2.0.0, Signature change on 2.5.0
pgr_bdAstar(other signatures) 2.5.0

Signature Summary¶

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

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

pgr_bdAstar(edges_sql, start_vid, end_vids [, directed, heuristic, factor, epsilon])
pgr_bdAstar(edges_sql, start_vids, end_vid [, directed, heuristic, factor, epsilon])
pgr_bdAstar(edges_sql, start_vids, end_vids [, directed, heuristic, factor, epsilon])

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

Using these signatures, will load once the graph and perform several one to one pgr_bdAstar

The result is the union of the results of the one to one pgr_bdAStar.
The extra start_vid and/or end_vid in the result is used to distinguish to which path it belongs.

Avaliability

pgr_bdAstar(one to one) 2.0, signature change on 2.5
pgr_bdAstar(other signatures) 2.5

Signatures¶

Minimal Signature¶

pgr_bdAstar(edges_sql, start_vid, end_vid)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)

This usage finds the shortest path from the start_vid to the end_vid

on a directed graph
with heuristic’s value 5
with factor’s value 1
with epsilon’s value 1

Example:	Using the defaults

SELECT * FROM pgr_bdAstar(
    'SELECT id, source, target, cost, reverse_cost, x1,y1,x2,y2
    FROM edge_table',
    2, 3
);
 seq | path_seq | node | edge | cost | agg_cost 
-----+----------+------+------+------+----------
   1 |        1 |    2 |    4 |    1 |        0
   2 |        2 |    5 |    8 |    1 |        1
   3 |        3 |    6 |    9 |    1 |        2
   4 |        4 |    9 |   16 |    1 |        3
   5 |        5 |    4 |    3 |    1 |        4
   6 |        6 |    3 |   -1 |    0 |        5
(6 rows)

pgr_bdAstar One to One¶

pgr_bdAstar(edges_sql, start_vid, end_vid, directed [, heuristic, factor, epsilon])
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)

This usage finds the shortest path from the start_vid to the end_vid allowing the user to choose

heuristic,
and/or factor
and/or epsilon.

Note

In the One to One signature, because of the deprecated signature existence, it is compulsory to indicate if the graph is directed or undirected.

Example:	Directed using Heuristic 2

SELECT * FROM pgr_bdAstar(
    'SELECT id, source, target, cost, reverse_cost, x1,y1,x2,y2
    FROM edge_table',
    2, 3,
    true, 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 |    9 |    1 |        2
   4 |        4 |    9 |   16 |    1 |        3
   5 |        5 |    4 |    3 |    1 |        4
   6 |        6 |    3 |   -1 |    0 |        5
(6 rows)

pgr_bdAstar One to many¶

pgr_bdAstar(edges_sql, start_vid, end_vids [, directed, heuristic, factor, epsilon])
RETURNS SET OF (seq, path_seq, end_vid, node, edge, cost, agg_cost) or EMPTY SET

This usage finds the shortest path from the start_vid to each end_vid in end_vids allowing the user to choose

if the graph is directed or undirected
and/or heuristic,
and/or factor
and/or epsilon.

Example:	Directed using Heuristic 3 and a factor of 3.5

SELECT * FROM pgr_bdAstar(
    'SELECT id, source, target, cost, reverse_cost, x1,y1,x2,y2
    FROM edge_table',
    2, ARRAY[3, 11],
    heuristic := 3, factor := 3.5
);
 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 |      11 |    2 |    4 |    1 |        0
   8 |        2 |      11 |    5 |    8 |    1 |        1
   9 |        3 |      11 |    6 |   11 |    1 |        2
  10 |        4 |      11 |   11 |   -1 |    0 |        3
(10 rows)

pgr_bdAstar Many to One¶

pgr_bdAstar(edges_sql, start_vids, end_vid [, directed, heuristic, factor, epsilon])
RETURNS SET OF (seq, path_seq, start_vid, node, edge, cost, agg_cost) or EMPTY SET

This usage finds the shortest path from each start_vid in start_vids to the end_vid allowing the user to choose

if the graph is directed or undirected
and/or heuristic,
and/or factor
and/or epsilon.

Example:	Undirected graph with Heuristic 4

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

pgr_bdAstar Many to Many¶

pgr_bdAstar(edges_sql, start_vids, end_vids [, directed, heuristic, factor, epsilon])
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost) or EMPTY SET

This usage finds the shortest path from each start_vid in start_vids to each end_vid in end_vids allowing the user to choose

if the graph is directed or undirected
and/or heuristic,
and/or factor
and/or epsilon.

Example:	Directed graph with a factor of 0.5

SELECT * FROM pgr_bdAstar(
    'SELECT id, source, target, cost, reverse_cost, x1,y1,x2,y2
    FROM edge_table',
    ARRAY[2, 7], ARRAY[3, 11],
    factor := 0.5
);
 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 |         2 |      11 |    2 |    4 |    1 |        0
|        2 |         2 |      11 |    5 |    8 |    1 |        1
|        3 |         2 |      11 |    6 |   11 |    1 |        2
|        4 |         2 |      11 |   11 |   -1 |    0 |        3
|        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 |         7 |      11 |    7 |    6 |    1 |        0
|        2 |         7 |      11 |    8 |    7 |    1 |        1
|        3 |         7 |      11 |    5 |   10 |    1 |        2
|        4 |         7 |      11 |   10 |   12 |    1 |        3
|        5 |         7 |      11 |   11 |   -1 |    0 |        4
(22 rows)

Description of the Signatures¶

Description of the edges_sql query for astar like functions¶

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

Description of the parameters of the signatures¶

Parameter	Type	Description
edges_sql	`TEXT`	Edges SQL query as described above.
start_vid	`ANY-INTEGER`	Starting vertex identifier.
start_vids	`ARRAY[ANY-INTEGER]`	Starting vertices identifierers.
end_vid	`ANY-INTEGER`	Ending vertex identifier.
end_vids	`ARRAY[ANY-INTEGER]`	Ending vertices identifiers.
directed	`BOOLEAN`	Optional. When `false` the graph is considered as Undirected. Default is `true` which considers the graph as Directed.
heuristic	`INTEGER`	(optional). 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`	(optional). For units manipulation. \(factor > 0\). Default `1`. see Factor
epsilon	`FLOAT`	(optional). For less restricted results. \(epsilon >= 1\). Default `1`.

Description of the return values for a path¶

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_id	`INT`	Path identifier. Has value 1 for the first of a path. Used when there are multiple paths for the same `start_vid` to `end_vid` combination.
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. Used when multiple starting vetrices are in the query.
end_vid	`BIGINT`	Identifier of the ending vertex. Used 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`.

pgRouting Manual (2.5)

pgr_bdAstar