pgr_bdAstar

pgr_bdAstar - Returns the shortest path using Bidirectional A* algorithm.

images/boost-inside.jpeg

Boost Graph Inside

Availability:

  • Version 3.2.0

    • New proposed function:

      • pgr_bdAstar(Combinations)

  • Version 3.0.0

    • Official function

  • Version 2.5.0

    • Signature change on pgr_bdAstar(One to One)

      • Old signature no longer supported

    • New Proposed functions:

      • pgr_bdAstar(One to Many)

      • pgr_bdAstar(Many to One)

      • pgr_bdAstar(Many to Many)

  • Version 2.0.0

    • Official pgr_bdAstar(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_bdAStar( One to One ) on the:

  • start_vid and end_vid in the result is used to distinguish to which path it belongs.

Signature

Summary 

pgr_bdAstar(Edges SQL, from_vid,  to_vid,  [, directed] [, heuristic] [, factor] [, epsilon])
pgr_bdAstar(Edges SQL, from_vid,  to_vids  [, directed] [, heuristic] [, factor] [, epsilon])
pgr_bdAstar(Edges SQL, from_vids, to_vid   [, directed] [, heuristic] [, factor] [, epsilon])
pgr_bdAstar(Edges SQL, from_vids, to_vids  [, directed] [, heuristic] [, factor] [, epsilon])
pgr_bdAstar(Edges SQL, Combinations SQL  [, directed] [, heuristic] [, factor] [, epsilon]) -- Proposed on v3.2

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_bdAstar(Edges SQL, start_vid, end_vid)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
Example :

From vertex \(2\) to vertex \(3\) on a directed graph 

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)

One to One 

pgr_bdAstar(Edges SQL, from_vid,  to_vid,  [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
Example :

From vertex \(2\) to vertex \(3\) on a directed graph 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)

One to many 

pgr_bdAstar(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 \(\{3, 11\}\) on a directed graph using heuristic \(3\) and factor \(3.5\) 

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)

Many to One 

pgr_bdAstar(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 \(\{2, 7\}\) to vertex \(3\) on an undirected graph using 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     8     1         2
   6         4          7     6     5     1         3
   7         5          7     3    -1     0         4
(7 rows)

Many to Many 

pgr_bdAstar(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 \(\{2, 7\}\) to vertices \(\{3, 11\}\) on a directed graph using factor \(0.5\) 

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         1
   3         3          2        3     6     9     1         2
   4         4          2        3     9    16     1         3
   5         5          2        3     4     3     1         4
   6         6          2        3     3    -1     0         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         1
  13         3          7        3     5     8     1         2
  14         4          7        3     6     9     1         3
  15         5          7        3     9    16     1         4
  16         6          7        3     4     3     1         5
  17         7          7        3     3    -1     0         6
  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)

Combinations 

pgr_bdAstar(Edges SQL, Combinations SQL  [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example :

Using a combinations table on a directed graph using factor \(0.5\) . 

SELECT * FROM pgr_bdAstar(
    'SELECT id, source, target, cost, reverse_cost, x1,y1,x2,y2
    FROM edge_table',
    'SELECT * FROM ( VALUES (2, 3), (7, 11) ) AS t(source, target)',
    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         1
   3         3          2        3     6     9     1         2
   4         4          2        3     9    16     1         3
   5         5          2        3     4     3     1         4
   6         6          2        3     3    -1     0         5
   7         1          7       11     7     6     1         0
   8         2          7       11     8     7     1         1
   9         3          7       11     5     8     1         2
  10         4          7       11     6    11     1         3
  11         5          7       11    11    -1     0         4
(11 rows)

Parameters

Parameter

Type

Description

Edges SQL

TEXT

Edges query as described below.

Combinations SQL

TEXT

Combinations query as described below.

from_vid

ANY-INTEGER

Starting vertex identifier. Parameter in:

from_vids

ARRAY[ANY-INTEGER]

Array of starting vertices identifiers. Parameter in:

to_vid

ANY-INTEGER

Ending vertex identifier. Parameter in:

to_vids

ARRAY[ANY-INTEGER]

Array of ending vertices identifiers. Parameter in:

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 queries

Edges query

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

Combinations query

Column

Type

Default

Description

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.

Where:

ANY-INTEGER :

SMALLINT, INTEGER, BIGINT

Result Columns

Returns set of (seq, path_id, 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. 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

Indices and tables