pgr_bdAstarCostMatrix

pgr_bdAstarCostMatrix - Calculates the a cost matrix using pgr_aStar .

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Boost Graph Inside

Availability

  • Version 3.0.0

    • Official function

  • Version 2.5.0

    • New Proposed function

Description

The main characteristics are:

  • Using internaly the pgr_bdAstar algorithm

  • Returns a cost matrix.

  • No ordering is performed

  • let v and u are nodes on the graph:

    • when there is no path from v to u :

      • no corresponding row is returned

      • cost from v to u is \(\inf\)

    • when \(v = u\) then

      • no corresponding row is returned

      • cost from v to u is \(0\)

  • When the graph is undirected the cost matrix is symmetric

Signatures

Summary 

pgr_bdAstarCostMatrix(edges_sql, vids [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)

Using defaults 

pgr_bdAstarCostMatrix(edges_sql, vids)
RETURNS SET OF (start_vid, end_vid, agg_cost)
Example :

Cost matrix for vertices \(\{1, 2, 3, 4\}\) on a directed graph 

SELECT * FROM pgr_bdAstarCostMatrix(
    'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
    (SELECT array_agg(id) FROM edge_table_vertices_pgr WHERE id < 5)
);
 start_vid  end_vid  agg_cost
-----------+---------+----------
         1        2         1
         1        3         6
         1        4         5
         2        1         1
         2        3         5
         2        4         4
         3        1         2
         3        2         1
         3        4         3
         4        1         3
         4        2         2
         4        3         1
(12 rows)

Complete Signature 

pgr_bdAstarCostMatrix(edges_sql, vids [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)
Example :

Symmetric cost matrix for vertices \(\{1, 2, 3, 4\}\) on an undirected graph using heuristic \(2\) 

SELECT * FROM pgr_bdAstarCostMatrix(
    'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
    (SELECT array_agg(id) FROM edge_table_vertices_pgr WHERE id < 5),
    false
);
 start_vid  end_vid  agg_cost
-----------+---------+----------
         1        2         1
         1        3         2
         1        4         3
         2        1         1
         2        3         1
         2        4         2
         3        1         2
         3        2         1
         3        4         1
         4        1         3
         4        2         2
         4        3         1
(12 rows)

Parameters

Parameter

Type

Description

edges_sql

TEXT

edges_sql inner query.

vids

ARRAY[ANY-INTEGER]

Array of vertices identifiers.

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 (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 :

Use with pgr_TSP 

SELECT * FROM pgr_TSP(
    $$
    SELECT * FROM pgr_bdAstarCostMatrix(
        'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
        (SELECT array_agg(id) FROM edge_table_vertices_pgr WHERE id < 5),
        false
    )
    $$,
    randomize := false
);
 seq  node  cost  agg_cost
-----+------+------+----------
   1     1     0         0
   2     2     1         1
   3     3     1         2
   4     4     1         3
   5     1     3         6
(5 rows)

See Also

Indices and tables