##  pgr_bdDijkstraCost 

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

Availability

• Version 3.2.0

• New proposed signature:

• Version 3.0.0

• Official function

• Version 2.5.0

• New proposed function

### Description

The  pgr_bdDijkstraCost  function sumarizes of the cost of the shortest path using the bidirectional Dijkstra Algorithm.

• Process is done only on edges with positive costs.

• A negative value on a cost column is interpreted as the edge does not exist.

• Values are returned when there is a path.

• When there is no path:

• When the starting vertex and ending vertex are the same.

• The aggregate cost of the non included values $$(v, v)$$ is $$0$$

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

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

• For optimization purposes, any duplicated value in the starting vertices or on the ending vertices are ignored.

• 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

• 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)  .

• Depending on the function and its parameters, the results can be symmetric.

• The aggregate cost of $$(u, v)$$ is the same as for $$(v, u)$$ .

• Any duplicated value in the start or end vertex identifiers are ignored.

• The returned values are ordered:

•  start_vid  ascending

•  end_vid  ascending

### Signatures

Summary

pgr_bdDijkstraCost( Edges SQL , start vid , end vid , [  directed  ])
pgr_bdDijkstraCost( Edges SQL , start vid , end vids , [  directed  ])
pgr_bdDijkstraCost( Edges SQL , start vids , end vid , [  directed  ])
pgr_bdDijkstraCost( Edges SQL , start vids , end vids , [  directed  ])
pgr_bdDijkstraCost( Edges SQL , Combinations SQL , [  directed  ])
RETURNS SET OF  (start_vid, end_vid, agg_cost) 
OR EMPTY SET

#### One to One

pgr_bdDijkstraCost( Edges SQL , start vid , end vid , [  directed  ])
RETURNS SET OF  (start_vid, end_vid, agg_cost) 
OR EMPTY SET
Example :

From vertex $$6$$ to vertex $$10$$ on a directed graph

SELECT * FROM pgr_bdDijkstraCost(
'SELECT id, source, target, cost, reverse_cost FROM edges',
6, 10, true);
start_vid  end_vid  agg_cost
-----------+---------+----------
6       10         5
(1 row)



#### One to Many

pgr_bdDijkstraCost( Edges SQL , start vid , end vids , [  directed  ])
RETURNS SET OF  (start_vid, end_vid, agg_cost) 
OR EMPTY SET
Example :

From vertex $$6$$ to vertices $$\{10, 17\}$$ on a directed graph

SELECT * FROM pgr_bdDijkstraCost(
'SELECT id, source, target, cost, reverse_cost FROM edges',
6, ARRAY[10, 17]);
start_vid  end_vid  agg_cost
-----------+---------+----------
6       10         5
6       17         4
(2 rows)



#### Many to One

pgr_bdDijkstraCost( Edges SQL , start vids , end vid , [  directed  ])
RETURNS SET OF  (start_vid, end_vid, agg_cost) 
OR EMPTY SET
Example :

From vertices $$\{6, 1\}$$ to vertex $$17$$ on a directed graph

SELECT * FROM pgr_bdDijkstraCost(
'SELECT id, source, target, cost, reverse_cost FROM edges',
ARRAY[6, 1], 17);
start_vid  end_vid  agg_cost
-----------+---------+----------
1       17         5
6       17         4
(2 rows)



#### Many to Many

pgr_bdDijkstraCost( Edges SQL , start vids , end vids , [  directed  ])
RETURNS SET OF  (start_vid, end_vid, agg_cost) 
OR EMPTY SET
Example :

From vertices $$\{6, 1\}$$ to vertices $$\{10, 17\}$$ on an undirected graph

SELECT * FROM pgr_bdDijkstraCost(
'SELECT id, source, target, cost, reverse_cost FROM edges',
ARRAY[6, 1], ARRAY[10, 17],
directed => false);
start_vid  end_vid  agg_cost
-----------+---------+----------
1       10         4
1       17         5
6       10         1
6       17         4
(4 rows)



#### Combinations

pgr_bdDijkstraCost( Edges SQL , Combinations SQL , [  directed  ])
RETURNS SET OF  (start_vid, end_vid, agg_cost) 
OR EMPTY SET
Example :

Using a combinations table on an undirected graph

The combinations table:

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



The query:

SELECT * FROM pgr_bdDijkstraCost(
'SELECT id, source, target, cost, reverse_cost FROM edges',
'SELECT source, target FROM combinations',
false);
start_vid  end_vid  agg_cost
-----------+---------+----------
5        6         1
5       10         2
6        5         1
6       15         2
(4 rows)



### Parameters

Column

Type

Description

 TEXT 

Edges SQL as described below

 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 .

### Inner Queries

#### Edges SQL

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  )

 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 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  .

Example 1 :

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

SELECT * FROM pgr_bdDijkstraCost(
'SELECT id, source, target, cost, reverse_cost 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_bdDijkstraCost(
'SELECT id, source, target, cost, reverse_cost 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_bdDijkstraCost(
'SELECT id, source, target, cost, reverse_cost 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)