pgr_aStarCostMatrix - proposed¶

Name¶

pgr_aStarCostMatrix - Calculates the a cost matrix using pgr_aStar.

Warning

These are proposed functions for next mayor release.

• They are not officially in the current release.
• They will likely officially be part of the next mayor release:
• The functions make use of ANY-INTEGER and ANY-NUMERICAL
• Name might not change. (But still can)
• Signature might not change. (But still can)
• Functionality might not change. (But still can)
• pgTap tests have being done. But might need more.
• Documentation might need refinement.

Availability: 2.4.0

Synopsis¶

Using aStar algorithm, calculate and return a cost matrix.

Signature Summary¶

pgr_aStarCostMatrix(edges_sql, vids)
pgr_aStarCostMatrix(edges_sql, vids, directed, heuristic, factor, epsilon)
RETURNS SET OF (start_vid, end_vid, agg_cost)


Signatures¶

Minimal Signature¶

The minimal signature:
• Is for a directed graph.
pgr_aStarCostMatrix(edges_sql, vids)
RETURNS SET OF (start_vid, end_vid, agg_cost)

Example: Cost matrix for vertices 1, 2, 3, and 4.
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: Cost matrix for an undirected graph for vertices 1, 2, 3, and 4.

This example returns a symmetric cost matrix.

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)



Description of the Signatures¶

Description of the edges_sql query for astar like functions¶

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 SMALLINT, INTEGER, BIGINT, REAL, FLOAT

Description of the parameters of the signatures¶

Parameter Type Description
edges_sql TEXT Edges SQL query as described above.
vids ARRAY[ANY-INTEGER] Array of vertices_identifiers.
directed BOOLEAN
• Optional.
• When false the graph is considered as Undirected.
• Default is true which considers the graph as Directed.
heuristic INTEGER

(optional). 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 (optional). For units manipulation. $$factor > 0$$. Default 1.
epsilon FLOAT (optional). For less restricted results. $$epsilon >= 1$$. Default 1.

Description of the return values for a Cost function¶

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.

Examples¶

Example: Use with 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)