pgr_bdAstarCostMatrix

pgr_bdAstarCostMatrix - Calculates the a cost matrix using pgr_aStar.

_images/boost-inside.jpeg

Boost Graph Inside

Availability

  • Official on v3.0.0
  • Proposed on v2.5.0

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_aStarCostMatrix(
    '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
-----------+---------+----------
         2 |       1 |        1
         3 |       1 |        2
         4 |       1 |        3
         1 |       2 |        1
         3 |       2 |        1
         4 |       2 |        2
         1 |       3 |        6
         2 |       3 |        5
         4 |       3 |        1
         1 |       4 |        5
         2 |       4 |        4
         3 |       4 |        3
(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_aStarCostMatrix(
    '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),
    directed := false, heuristic := 2
);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         2 |       1 |        1
         3 |       1 |        2
         4 |       1 |        3
         1 |       2 |        1
         3 |       2 |        1
         4 |       2 |        2
         1 |       3 |        2
         2 |       3 |        1
         4 |       3 |        1
         1 |       4 |        3
         2 |       4 |        2
         3 |       4 |        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. 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.
agg_cost FLOAT Aggregate cost from start_vid to end_vid.

Additional Examples

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