pgr_aStarCostMatrix¶

pgr_aStarCostMatrix - Calculates the a cost matrix using pgr_aStar.

Boost Graph Inside

Availability

Version 3.0.0
- Official function
Version 2.4.0
- New proposed function

Support

Description¶

The main characteristics are:

Using internaly the pgr_aStar 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_aStarCostMatrix(edges_sql, vids [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)

Using defaults

pgr_aStarCostMatrix(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
-----------+---------+----------
         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_aStarCostMatrix(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
-----------+---------+----------
         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. 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)