pgr_bdAstar

Name

pgr_bdAstar — Returns the shortest path using A* algorithm.

_images/boost-inside.jpeg

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 |        3
   3 |        3 |    6 |    9 |    1 |        5
   4 |        4 |    9 |   16 |    1 |        8
   5 |        5 |    4 |    3 |    1 |        9
   6 |        6 |    3 |   -1 |    0 |       10
(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 |        2
   3 |        3 |    6 |    9 |    1 |        3
   4 |        4 |    9 |   16 |    1 |        4
   5 |        5 |    4 |    3 |    1 |        5
   6 |        6 |    3 |   -1 |    0 |        6
(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 |     25.5
   3 |        3 |       3 |    6 |    9 |    1 |    38.75
   4 |        4 |       3 |    9 |   16 |    1 |    64.25
   5 |        5 |       3 |    4 |    3 |    1 |    65.25
   6 |        6 |       3 |    3 |   -1 |    0 |    66.25
   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 | 3.23606797749979
   5 |        3 |         7 |    5 |    8 |    1 | 5.65028153987288
   6 |        4 |         7 |    6 |    5 |    1 | 6.65028153987288
   7 |        5 |         7 |    3 |   -1 |    0 | 7.65028153987288
(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 |        1 |         2 |       3 |    2 |    4 |    1 |        0
   2 |        2 |         2 |       3 |    5 |    8 |    1 |        2
   3 |        3 |         2 |       3 |    6 |    9 |    1 |      3.5
   4 |        4 |         2 |       3 |    9 |   16 |    1 |      4.5
   5 |        5 |         2 |       3 |    4 |    3 |    1 |      5.5
   6 |        6 |         2 |       3 |    3 |   -1 |    0 |      6.5
   7 |        1 |         2 |      11 |    2 |    4 |    1 |        0
   8 |        2 |         2 |      11 |    5 |    8 |    1 |        1
   9 |        3 |         2 |      11 |    6 |   11 |    1 |        2
  10 |        4 |         2 |      11 |   11 |   -1 |    0 |        3
  11 |        1 |         7 |       3 |    7 |    6 |    1 |        0
  12 |        2 |         7 |       3 |    8 |    7 |    1 |      2.5
  13 |        3 |         7 |       3 |    5 |    8 |    1 |      4.5
  14 |        4 |         7 |       3 |    6 |    9 |    1 |        6
  15 |        5 |         7 |       3 |    9 |   16 |    1 |        7
  16 |        6 |         7 |       3 |    4 |    3 |    1 |        8
  17 |        7 |         7 |       3 |    3 |   -1 |    0 |        9
  18 |        1 |         7 |      11 |    7 |    6 |    1 |        0
  19 |        2 |         7 |      11 |    8 |    7 |    1 |        1
  20 |        3 |         7 |      11 |    5 |    8 |    1 |        2
  21 |        4 |         7 |      11 |    6 |   11 |    1 |        3
  22 |        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.