• Supported versions: Latest (3.3) 3.2 3.1 3.0

• Unsupported versions: 2.6 2.5

pgr_bdAstarCost

pgr_bdAstarCost - Total cost of the shortest path(s) using the bidirectional A* algorithm.

Boost Graph Inside

Availability

• Version 3.2.0

  • New proposed signature:

    • pgr_bdAstarCost (Combinations)

• Version 3.0.0

  • Official function

• Version 2.4.0

  • New proposed function

Description

The pgr_bdAstarCost function sumarizes of the cost of the shortest path(s) using the bidirectional A* algorithm.

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: \(O((E + V) * \log V)\)

• It does not return a path.

• Returns the sum of the costs of the shortest path of each pair combination of nodes requested.

• Let be the case the values returned are stored in a table, so the unique index would be the pair: (start_vid, end_vid)

• For undirected graphs, the results are symmetric.

  • The agg_cost of (u, v) is the same as for (v, u).

• The returned values are ordered in ascending order:

  • start_vid ascending

  • end_vid ascending

Signatures

Summary

pgr_bdAstarCost(Edges SQL, start vid, end vid [, directed] [, heuristic] [, factor] [, epsilon])
pgr_bdAstarCost(Edges SQL, start vid, end vids [, directed] [, heuristic] [, factor] [, epsilon])
pgr_bdAstarCost(Edges SQL, start vids, end vid [, directed] [, heuristic] [, factor] [, epsilon])
pgr_bdAstarCost(Edges SQL, start vids, end vids [, directed] [, heuristic] [, factor] [, epsilon])
pgr_bdAstarCost(Edges SQL, Combinations SQL  [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

One to One

pgr_bdAstarCost(Edges SQL, start vid, end vid [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Example

From vertex \(2\) to vertex \(11\) on a directed graph with heuristic \(2\)

SELECT * FROM pgr_bdAstarCost(
  'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
  FROM edge_table',
  2, 11,
  directed => true, heuristic => 2
);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         2 |      11 |        3
(1 row)

One to Many

pgr_bdAstarCost(Edges SQL, start vid, end vids [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Example

From vertex \(2\) to vertices \(\{3, 11\}\) on a directed graph with heuristic \(3\) and factor \(3.5\)

SELECT * FROM pgr_bdAstarCost(
  'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
  FROM edge_table',
  2, ARRAY[3, 11],
  heuristic => 3, factor := 3.5
);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         2 |       3 |        5
         2 |      11 |        3
(2 rows)

Many to One

pgr_bdAstarCost(Edges SQL, start vids, end vid [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Example

From vertices \(\{2, 10\}\) to vertex \(3\) on an undirected graph with heuristic \(4\)

SELECT * FROM pgr_bdAstarCost(
  'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
  FROM edge_table',
  ARRAY[2, 10], 3,
  false, heuristic => 4
);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         2 |       3 |        1
        10 |       3 |        3
(2 rows)

Many to Many

pgr_bdAstarCost(Edges SQL, start vids, end vids [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Example

From vertices \(\{2, 10\}\) to vertices \(\{3, 11\}\) on a directed graph with factor \(0.5\)

SELECT * FROM pgr_bdAstarCost(
  'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
  FROM edge_table',
  ARRAY[2, 10], ARRAY[3, 11],
  factor => 0.5
);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         2 |       3 |        5
         2 |      11 |        3
        10 |       3 |        5
        10 |      11 |        1
(4 rows)

Combinations

pgr_bdAstarCost(Edges SQL, Combinations SQL  [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Example

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

The combinations table:

SELECT * FROM combinations_table;
 source | target
--------+--------
      1 |      2
      1 |      3
      2 |      1
      2 |      4
      2 |     17
(5 rows)

The query:

SELECT * FROM pgr_bdAstarCost(
  'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
  FROM edge_table',
  'SELECT * FROM combinations_table',
  factor => 0.5
);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         1 |       2 |        1
         1 |       3 |        6
         2 |       1 |        1
         2 |       4 |        4
(4 rows)

Parameters

Column	Type	Description
Edges SQL	TEXT	Edges SQL as described below
Combinations SQL	TEXT	Combinations SQL as described below
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.

Optional parameters

Column	Type	default	Description
directed	BOOLEAN	true	When true the graph is considered Directed When false the graph is considered as Undirected.

aStar optional Parameters

Parameter	Type	Default	Description
heuristic	INTEGER	5	Heuristic number. Current valid values 0~5. 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 SQL

Parameter	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 SQL

Parameter	Type	Description
source	ANY-INTEGER	Identifier of the departure vertex.
target	ANY-INTEGER	Identifier of the arrival vertex.

Where:

ANY-INTEGER

SMALLINT, INTEGER, BIGINT

Return Columns

Set of (start_vid, end_vid, agg_cost)

Column	Type	Description
start_vid	BIGINT	Identifier of the starting vertex.
end_vid	BIGINT	Identifier of the ending vertex.
agg_cost	FLOAT	Aggregate cost from start_vid to end_vid.

Additional Examples

Example 1

Demonstration of repeated values are ignored, and result is sorted.

 SELECT * FROM pgr_bdAstarCost(
  'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
  FROM edge_table',
  ARRAY[5, 3, 4, 3, 3, 4], ARRAY[3, 5, 3, 4]);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         3 |       4 |        3
         3 |       5 |        2
         4 |       3 |        1
         4 |       5 |        3
         5 |       3 |        4
         5 |       4 |        3
(6 rows)

Example 2

Making start_vids the same as end_vids.

SELECT * FROM pgr_bdAstarCost(
  'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
  FROM edge_table',
  ARRAY[5, 3, 4], ARRAY[5, 3, 4]);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         3 |       4 |        3
         3 |       5 |        2
         4 |       3 |        1
         4 |       5 |        3
         5 |       3 |        4
         5 |       4 |        3
(6 rows)

Example 3

Manually assigned vertex combinations.

SELECT * FROM pgr_bdAstarCost(
  'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
  FROM edge_table',
  'SELECT * FROM (VALUES (2, 3), (2, 5), (11, 3)) AS combinations (source, target)');
 start_vid | end_vid | agg_cost
-----------+---------+----------
         2 |       3 |        5
         2 |       5 |        1
        11 |       3 |        4
(3 rows)

See Also

• Bidirectional A* - Family of functions

• Cost - Category

• Sample Data

Indices and tables

• Index

• Search Page