pgr_aStarCost¶

pgr_aStarCost - Total cost of the shortest path(s) using the A* algorithm.

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

Availability

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

Description¶

The pgr_aStarCost function sumarizes of the cost of the shortest path(s) using the A* algorithm.

The main characteristics are:

Process works for directed and undirected graphs.
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 \(0\)
When \((x,y)\) coordinates for the same vertex identifier differ:
- A random selection of the vertex’s \((x,y)\) coordinates is used.
Running time: \(O((E + V) * \log V)\)

It does not return a path.
Returns the sum of the costs of the shortest path of each pair combination of nodes requested.
Let be the case the values returned are stored in a table, so the unique index would be the pair: (start_vid, end_vid)
For undirected graphs, the results are symmetric.
- The agg_cost of (u, v) is the same as for (v, u).
The returned values are ordered in ascending order:
- start_vid ascending
- end_vid ascending

Signatures¶

Summary

pgr_aStarCost(Edges SQL, start vid, end vid, [options])
pgr_aStarCost(Edges SQL, start vid, end vids, [options])
pgr_aStarCost(Edges SQL, start vids, end vid, [options])
pgr_aStarCost(Edges SQL, start vids, end vids, [options])
pgr_aStarCost(Edges SQL, Combinations SQL, [options])
options: [directed, heuristic, factor, epsilon]

RETURNS SET OF (start_vid, end_vid, agg_cost)

OR EMPTY SET

One to One¶

pgr_aStarCost(Edges SQL, start vid, end vid, [options])

options: [directed, heuristic, factor, epsilon]

RETURNS SET OF (start_vid, end_vid, agg_cost)

OR EMPTY SET

Example:: From vertex \(6\) to vertex \(12\) on a directed graph with heuristic \(2\)

SELECT * FROM pgr_aStarCost(
  'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
  FROM edges',
  6, 12,
  directed => true, heuristic => 2);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         6 |      12 |        3
(1 row)

One to Many¶

pgr_aStarCost(Edges SQL, start vid, end vids, [options])

options: [directed, heuristic, factor, epsilon]

RETURNS SET OF (start_vid, end_vid, agg_cost)

OR EMPTY SET

Example:: From vertex \(6\) to vertices \(\{10, 12\}\) on a directed graph with heuristic \(3\) and factor \(3.5\)

SELECT * FROM pgr_aStarCost(
  'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
  FROM edges',
  6, ARRAY[10, 12],
  heuristic => 3, factor => 3.5);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         6 |      10 |        5
         6 |      12 |        3
(2 rows)

Many to One¶

pgr_aStarCost(Edges SQL, start vids, end vid, [options])

options: [directed, heuristic, factor, epsilon]

RETURNS SET OF (start_vid, end_vid, agg_cost)

OR EMPTY SET

Example:: From vertices \(\{6, 8\}\) to vertex \(10\) on an undirected graph with heuristic \(4\)

SELECT * FROM pgr_aStarCost(
  'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
  FROM edges',
  ARRAY[6, 8], 10,
  false, heuristic => 4);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         6 |      10 |        1
         8 |      10 |        3
(2 rows)

Many to Many¶

pgr_aStarCost(Edges SQL, start vids, end vids, [options])

options: [directed, heuristic, factor, epsilon]

RETURNS SET OF (start_vid, end_vid, agg_cost)

OR EMPTY SET

Example:: From vertices \(\{6, 8\}\) to vertices \(\{10, 12\}\) on a directed graph with factor \(0.5\)

SELECT * FROM pgr_aStarCost(
  'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
  FROM edges',
  ARRAY[6, 8], ARRAY[10, 12],
  factor => 0.5);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         6 |      10 |        5
         6 |      12 |        3
         8 |      10 |        5
         8 |      12 |        1
(4 rows)

Combinations¶

pgr_aStarCost(Edges SQL, Combinations SQL, [options])

options: [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 with factor \(0.5\).

The combinations table:

SELECT * FROM combinations;
 source | target
--------+--------
      5 |      6
      5 |     10
      6 |      5
      6 |     15
      6 |     14
(5 rows)

The query:

SELECT * FROM pgr_aStarCost(
  'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
  FROM edges',
  'SELECT * FROM combinations',
  factor => 0.5);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         5 |       6 |        1
         5 |      10 |        6
         6 |       5 |        1
         6 |      15 |        4
(4 rows)

Parameters¶

Column	Type	Description
Edges SQL	`TEXT`	Edges SQL as described below
Combinations SQL	`TEXT`	Combinations SQL as described below
start vid	`BIGINT`	Identifier of the starting vertex of the path.
start vids	`ARRAY[BIGINT]`	Array of identifiers of starting vertices.
end vid	`BIGINT`	Identifier of the ending vertex of the path.
end vids	`ARRAY[BIGINT]`	Array of identifiers of ending 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. \(epsilon >= 1\).

Parameter

Type

Default

Description

heuristic

INTEGER

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

Combinations SQL¶

Parameter	Type	Description
`source`	ANY-INTEGER	Identifier of the departure vertex.
`target`	ANY-INTEGER	Identifier of the arrival vertex.

Where:

ANY-INTEGER:: SMALLINT, INTEGER, BIGINT

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 1:: Demonstration of repeated values are ignored, and result is sorted.

 SELECT * FROM pgr_aStarCost(
  'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
  FROM edges',
  ARRAY[7, 10, 15, 10, 10, 15], ARRAY[10, 7, 10, 15]);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         7 |      10 |        4
         7 |      15 |        3
        10 |       7 |        2
        10 |      15 |        3
        15 |       7 |        3
        15 |      10 |        1
(6 rows)

Example 2:: Making start vids the same as end vids.

SELECT * FROM pgr_aStarCost(
  'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
  FROM edges',
  ARRAY[7, 10, 15], ARRAY[7, 10, 15]);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         7 |      10 |        4
         7 |      15 |        3
        10 |       7 |        2
        10 |      15 |        3
        15 |       7 |        3
        15 |      10 |        1
(6 rows)

Example 3:: Manually assigned vertex combinations.

SELECT * FROM pgr_aStarCost(
  'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
  FROM edges',
  'SELECT * FROM (VALUES (6, 10), (6, 7), (12, 10)) AS combinations (source, target)');
 start_vid | end_vid | agg_cost
-----------+---------+----------
         6 |       7 |        1
         6 |      10 |        5
        12 |      10 |        4
(3 rows)

pgr_aStarCost¶

Description¶

Signatures¶

One to One¶

One to Many¶

Many to One¶

Many to Many¶

Combinations¶

Parameters¶

Optional parameters¶

aStar optional Parameters¶

Inner Queries¶

Edges SQL¶

Combinations SQL¶

Result Columns¶

Additional Examples¶

See Also¶