pgr_aStarCostMatrix

pgr_aStarCostMatrix - Calculates the a cost matrix using pgr_aStar.

_images/boost-inside.jpeg

Boost Graph Inside

Availability

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, start vids
    [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)
Example:Symmetric cost matrix for vertices \(\{5, 6, 10, 15\}\) on an undirected graph using heuristic \(2\) 
SELECT * FROM pgr_aStarCostMatrix(
  'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edges',
  (SELECT array_agg(id) FROM vertices WHERE id IN (5, 6, 10, 15)),
  directed => false, heuristic => 2);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         5 |       6 |        1
         5 |      10 |        2
         5 |      15 |        3
         6 |       5 |        1
         6 |      10 |        1
         6 |      15 |        2
        10 |       5 |        2
        10 |       6 |        1
        10 |      15 |        1
        15 |       5 |        3
        15 |       6 |        2
        15 |      10 |        1
(12 rows)

Parameters

Column Type Description
Edges SQL TEXT Edges SQL as described below
start vids ARRAY[BIGINT] Array of identifiers of starting 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: \(h(v) = abs(max(\Delta x, \Delta y))\)
  • 2: \(h(v) = abs(min(\Delta x, \Delta y))\)
  • 3: \(h(v) = \Delta x * \Delta x + \Delta y * \Delta y\)
  • 4: \(h(v) = sqrt(\Delta x * \Delta x + \Delta y * \Delta y)\)
  • 5: \(h(v) = abs(\Delta x) + abs(\Delta y)\)
factor FLOAT 1 For units manipulation. \(factor > 0\).
epsilon FLOAT 1 For less restricted results. \(epsilon >= 1\).

See heuristics available and factor handling.

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

Result 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:Use with pgr_TSP 
SELECT * FROM pgr_TSP(
  $$
  SELECT * FROM pgr_aStarCostMatrix(
    'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edges',
    (SELECT array_agg(id) FROM vertices WHERE id IN (5, 6, 10, 15)),
    directed=> false, heuristic => 2)
  $$,
  randomize => false
);
NOTICE:  pgr_TSP no longer solving with simulated annaeling
HINT:  Ignoring annaeling parameters
 seq | node | cost | agg_cost
-----+------+------+----------
   1 |    5 |    0 |        0
   2 |    6 |    1 |        1
   3 |   10 |    1 |        2
   4 |   15 |    1 |        3
   5 |    5 |    3 |        6
(5 rows)