# pgr_bdAstarCost¶

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

Availability

• Version 3.0.0
• Official function
• Version 2.5.0
• New Proposed function

## Description¶

• 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: $$O((E + V) * \log V)$$

## Signatures¶

Summary

pgr_bdAstarCost(edges_sql, from_vid,  to_vid  [, directed] [, heuristic] [, factor] [, epsilon])
pgr_bdAstarCost(edges_sql, from_vid,  to_vids [, directed] [, heuristic] [, factor] [, epsilon])
pgr_bdAstarCost(edges_sql, from_vids, to_vid  [, directed] [, heuristic] [, factor] [, epsilon])
pgr_bdAstarCost(edges_sql, from_vids, to_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.

Using defaults

pgr_bdAstarCost(edges_sql, from_vid,  to_vid)
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Example: From vertex $$2$$ to vertex $$3$$ on a directed graph
SELECT * FROM pgr_bdAstarCost(
'SELECT id, source, target, cost, reverse_cost, x1,y1,x2,y2
FROM edge_table',
2, 3
);
start_vid | end_vid | agg_cost
-----------+---------+----------
2 |       3 |        5
(1 row)



### One to One¶

pgr_bdAstarCost(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 $$3$$ on an directed graph using heuristic $$2$$
SELECT * FROM pgr_bdAstarCost(
'SELECT id, source, target, cost, reverse_cost, x1,y1,x2,y2
FROM edge_table',
2, 3,
true, heuristic := 2
);
start_vid | end_vid | agg_cost
-----------+---------+----------
2 |       3 |        5
(1 row)



### One to many¶

pgr_bdAstarCost(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 $$\{3, 11\}$$ on a directed graph using heuristic 3 and factor $$3.5$$
SELECT * FROM pgr_bdAstarCost(
'SELECT id, source, target, cost, reverse_cost, x1,y1,x2,y2
FROM edge_table',
2, ARRAY[3, 11],
heuristic := 3, factor := 3.5
);
start_vid | end_vid | agg_cost
-----------+---------+----------
2 |       3 |        5
2 |      11 |        3
(2 rows)



### Many to One¶

pgr_bdAstarCost(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 $$3$$ on a undirected graph using heuristic $$4$$
SELECT * FROM pgr_bdAstarCost(
'SELECT id, source, target, cost, reverse_cost, x1,y1,x2,y2
FROM edge_table',
ARRAY[2, 7], 3,
false, heuristic := 4
);
start_vid | end_vid | agg_cost
-----------+---------+----------
2 |       3 |        1
7 |       3 |        4
(2 rows)



### Many to Many¶

pgr_bdAstarCost(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 $$\{3, 11\}$$ on a directed using heuristic $$5$$ and factor $$0.5$$
SELECT * FROM pgr_bdAstarCost(
'SELECT id, source, target, cost, reverse_cost, x1,y1,x2,y2
FROM edge_table',
ARRAY[2, 7], ARRAY[3, 11],
factor := 0.5
);
start_vid | end_vid | agg_cost
-----------+---------+----------
2 |       3 |        5
2 |      11 |        3
7 |       3 |        6
7 |      11 |        4
(4 rows)



## Parameters¶

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

Starting vertex identifier. Parameter in:

from_vids ARRAY[ANY-INTEGER]

Array of starting vertices identifiers. Parameter in:

to_vid ANY-INTEGER

Ending vertex identifier. Parameter in:

to_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 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.