pgr_aStarCost

Synopsis

pgr_aStarCost — Returns the aggregate cost shortest path using pgr_aStar algorithm.

_images/boost-inside.jpeg

Boost Graph Inside

Characteristics

  • Default kind of graph is directed when
    • directed flag is missing.
    • directed flag is set to true
  • Unless specified otherwise, ordering is:
    • first by start_vid (if exists)
    • then by end_vid
  • Values are returned when there is a path
  • Let \(v\) and \(u\) be nodes on the graph:
    • If there is no path from \(v\) to \(u\):
      • no corresponding row is returned
      • agg_cost from \(v\) to \(u\) is \(\infty\)
    • There is no path when \(v = u\) therefore
      • no corresponding row is returned
      • agg_cost from v to u is \(0\)
  • Edges with negative costs are not included in the graph.
  • When (x,y) coordinates for the same vertex identifier differ:
    • A random selection of the vertex’s (x,y) coordinates is used.
  • Running time: \(O((E + V) * \log V)\)

Availability

  • New in v2.4.0

Signature Summary

pgr_aStarCost(edges_sql, start_vid, end_vid)
pgr_aStarCost(edges_sql, start_vid, end_vid [, directed, heuristic, factor, epsilon])
pgr_aStarCost(edges_sql, start_vid, end_vids [, directed, heuristic, factor, epsilon])
pgr_aStarCost(edges_sql, starts_vid, end_vid [, directed, heuristic, factor, epsilon])
pgr_aStarCost(edges_sql, starts_vid, end_vids [, directed, heuristic, factor, epsilon])

RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET

Optional parameters are named parameters and have a default value.

Minimal Signature

pgr_aStarCost(edges_sql, start_vid, end_vid)
RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET
Example:Using the defaults
SELECT * FROM pgr_aStarCost(
    'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
    2, 12);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         2 |      12 |        4
(1 row)

One to One

pgr_aStarCost(edges_sql, start_vid, end_vid [, directed, heuristic, factor, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET
Example:Using heuristic 2
SELECT * FROM pgr_aStarCost(
    'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
    2, 12,
    directed := false, heuristic := 2);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         2 |      12 |        4
(1 row)

One to many

pgr_aStarCost(edges_sql, start_vid, end_vids [, directed, heuristic, factor, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET
Example:From vertex 2 to vertices \(\{3, 12\}\) using heuristic 2
SELECT * FROM pgr_aStarCost(
    'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
    2, ARRAY[3, 12], heuristic := 2);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         2 |       3 |        5
         2 |      12 |        4
(2 rows)

Many to One

pgr_aStarCost(edges_sql, start_vids, end_vid [, directed, heuristic, factor, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET
Example:From vertices \(\{2, 7\}\) to vertex \(12\) using heuristic 0
SELECT * FROM pgr_aStarCost(
    'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
    ARRAY[7, 2], 12, heuristic := 0);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         2 |      12 |        4
         7 |      12 |        5
(2 rows)

Many to Many

pgr_aStarCost(edges_sql, start_vids, end_vids [, directed, heuristic, factor, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET
Example:From vertices \(\{2, 7\}\) to vertices \(\{3, 12\}\) using heuristic 2
SELECT * FROM pgr_aStarCost(
    'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
    ARRAY[7, 2], ARRAY[3, 12], heuristic := 2);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         2 |       3 |        5
         2 |      12 |        4
         7 |       3 |        6
         7 |      12 |        5
(4 rows)

Parameters

Parameter Type Description
edges_sql TEXT edges_sql inner query.
start_vid ANY-INTEGER

Starting vertex identifier. Parameter in:

start_vids ARRAY[ANY-INTEGER]

Array of starting vertices identifiers. Parameter in:

end_vid ANY-INTEGER

Ending vertex identifier. Parameter in:

end_vids ARRAY[ANY-INTEGER]

Array of ending vertices identifiers. Parameter in:

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.