## pgr_bdDijkstraCost

 pgr_bdDijkstraCost  - Returns the shortest path(s)’s cost using Bidirectional Dijkstra algorithm.

Availability:

• Version 3.2.0

• New proposed function:

• pgr_bdDijkstraCost(Combinations)

• Version 3.0.0

• Official function

• Version 2.5.0

• New proposed function

### Description

The main characteristics are:

• Process is done only on edges with positive costs.

• Values are returned when there is a path.

• When the starting vertex and ending vertex are the same, there is no path.

• The agg_cost the non included values (v, v) is 0

• When the starting vertex and ending vertex are the different and there is no path:

• The agg_cost the non included values (u, v) is $$\infty$$

• Running time (worse case scenario): $$O((V \log V + E))$$

• For large graphs where there is a path bewtween the starting vertex and ending vertex:

• It is expected to terminate faster than pgr_dijkstra

### Signatures

Summary

pgr_bdDijkstraCost(Edges SQL, from_vid,  to_vid  [, directed])
pgr_bdDijkstraCost(Edges SQL, from_vid,  to_vids [, directed])
pgr_bdDijkstraCost(Edges SQL, from_vids, to_vid  [, directed])
pgr_bdDijkstraCost(Edges SQL, from_vids, to_vids [, directed])
pgr_bdDijkstraCost(Edges SQL, Combinations SQL [, directed])

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


Using default

pgr_bdDijkstraCost(Edges SQL, from_vid,  to_vid)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET

Example :

From vertex $$2$$ to vertex $$3$$ on a directed graph

SELECT * FROM pgr_bdDijkstraCost(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, 3
);
start_vid  end_vid  agg_cost
-----------+---------+----------
2        3         5
(1 row)



#### One to One

pgr_bdDijkstraCost(Edges SQL, from_vid,  to_vid  [, directed])
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET

Example :

From vertex $$2$$ to vertex $$3$$ on an undirected graph

SELECT * FROM pgr_bdDijkstraCost(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, 3,
false
);
start_vid  end_vid  agg_cost
-----------+---------+----------
2        3         1
(1 row)



#### One to Many

pgr_bdDijkstraCost(Edges SQL, from_vid,  to_vids [, directed])
RETURNS SET OF (seq, path_seq, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET

Example :

From vertex $$2$$ to vertices $$\{3, 11\}$$ on a directed graph

SELECT * FROM pgr_bdDijkstraCost(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, ARRAY[3, 11]);
start_vid  end_vid  agg_cost
-----------+---------+----------
2        3         5
2       11         3
(2 rows)



#### Many to One

pgr_bdDijkstraCost(Edges SQL, from_vids, to_vids [, directed])
RETURNS SET OF (seq, path_seq, start_vid, node, edge, cost, agg_cost)
OR EMPTY SET

Example :

From vertices $$\{2, 7\}$$ to vertex $$3$$ on a directed graph

SELECT * FROM pgr_bdDijkstraCost(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2, 7], 3);
start_vid  end_vid  agg_cost
-----------+---------+----------
2        3         5
7        3         6
(2 rows)



#### Many to Many

pgr_bdDijkstraCost(Edges SQL, start_vids, end_vids [, directed])
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET

Example :

From vertices $$\{2, 7\}$$ to vertices $$\{3, 11\}$$ on a directed graph

SELECT * FROM pgr_bdDijkstraCost(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2, 7], ARRAY[3, 11]);
start_vid  end_vid  agg_cost
-----------+---------+----------
2        3         5
2       11         3
7        3         6
7       11         4
(4 rows)



#### Combinations

pgr_bdDijkstra(Edges SQL, Combinations SQL [, directed])
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET

Example :

Using a combinations table on a directed graph.

SELECT * FROM pgr_bdDijkstraCost(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
'SELECT * FROM ( VALUES (2, 3), (7, 11) ) AS t(source, target)');
start_vid  end_vid  agg_cost
-----------+---------+----------
2        3         5
7       11         4
(2 rows)



### Parameters

Parameter

Type

Default

Description

Edges SQL

 TEXT 

Edges query as described below

Combinations SQL

 TEXT 

Combinations query 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.

directed

 BOOLEAN 

 true 

• When  true  Graph is considered Directed

• When  false  the graph is considered as Undirected .

### Inner queries

#### Edges query

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.

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.

Where:

ANY-INTEGER :

SMALLINT, INTEGER, BIGINT

### Result Columns

Returns 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  .