pgr_aStarCost¶

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

_images/boost-inside.jpeg — Boost Graph Inside¶

Availability

Version 3.2.0
- New proposed function:
  - pgr_aStarCost(Combinations)
Version 3.0.0
- Official function
Version 2.4.0
- New proposed function

Description¶

The main characteristics are:

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: \(O((E + V) * \log V)\)

The results are equivalent to the union of the results of the pgr_aStarCost( One to One ) on the:
- pgr_aStarCost( One to Many )
- pgr_aStarCost( Many to One )
- pgr_aStarCost( Many to Many )

Signatures¶

Summary

pgr_aStarCost(Edges SQL, from_vid,  to_vid   [, directed] [, heuristic] [, factor] [, epsilon])
pgr_aStarCost(Edges SQL, from_vid,  to_vids  [, directed] [, heuristic] [, factor] [, epsilon])
pgr_aStarCost(Edges SQL, from_vids, to_vid   [, directed] [, heuristic] [, factor] [, epsilon])
pgr_aStarCost(Edges SQL, from_vids, to_vids  [, directed] [, heuristic] [, factor] [, epsilon])
pgr_aStarCost(Edges SQL, Combinations SQL  [, directed] [, heuristic] [, factor] [, epsilon]) -- Proposed on v3.2

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

Optional parameters are named parameters and have a default value.

Using defaults

pgr_aStarCost(Edges SQL, start_vid, end_vid)
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Example: From vertex \(2\) to vertex \(12\) on a directed graph

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, from_vid,  to_vid   [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Example: From vertex \(2\) to vertex \(12\) on an undirected graph 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, from_vid,  to_vids  [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Example: From vertex \(2\) to vertices \(\{3, 12\}\) on a directed graph 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, from_vids, to_vid   [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Example: From vertices \(\{7, 2\}\) to vertex \(12\) on a directed graph 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, from_vids, to_vids  [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Example: From vertices \(\{7, 2\}\) to vertices \(\{3, 12\}\) on a directed graph 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)

Combinations¶

pgr_aStarCost(Edges SQL, Combinations SQL  [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Example: Using a combinations table on a directed graph using heuristic \(2\).

SELECT * FROM pgr_aStarCost(
    'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
    'SELECT * FROM ( VALUES (7, 3), (2, 12) ) AS t(source, target)',
    heuristic := 2);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         2 |      12 |        4
         7 |       3 |        6
(2 rows)

Parameters¶

Parameter	Type	Description
Edges SQL	`TEXT`	Edges query as described below.
Combinations SQL	`TEXT`	Combinations query as described below.
from_vid	`ANY-INTEGER`	Starting vertex identifier. Parameter in: One to One One to Many
from_vids	`ARRAY[ANY-INTEGER]`	Array of starting vertices identifiers. Parameter in: Many to One Many to Many
to_vid	`ANY-INTEGER`	Ending vertex identifier. Parameter in: One to One Many to One
to_vids	`ARRAY[ANY-INTEGER]`	Array of ending vertices identifiers. Parameter in: One to Many Many to Many

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 queries¶

Edges query¶

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

Combinations query¶

Column	Type	Default	Description
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.