## pgr_dijkstraCost

 pgr_dijkstraCost 

Using Dijkstra algorithm implemented by Boost.Graph, and extract only the aggregate cost of the shortest path(s) found, for the combination of vertices given.

Availability

• Version 3.1.0

• New Proposed functions:

• pgr_dijkstraCost(combinations)

• Version 2.2.0

• New Official function

### Description

The  pgr_dijkstraCost  algorithm, is a good choice to calculate the sum of the costs of the shortest path for a subset of pairs of nodes of the graph. We make use of the Boost’s implementation of dijkstra which runs in $$O(V \log V + E)$$ time.

The main characteristics are:
• It does not return a path.

• Returns the sum of the costs of the shortest path for pair combination of nodes in the graph.

• Process is done only on edges with positive costs.

• Values are returned when there is a path.

• The returned values are in the form of a set of (start_vid, end_vid, agg_cost) .

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

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

• 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) .

• Any duplicated value in the start_vids or end_vids is ignored.

• The returned values are ordered:

• start_vid ascending

• end_vid ascending

• Running time: $$O( start\_vids * (V \log V + E))$$

### Signatures

Summary

pgr_dijkstraCost(edges_sql, from_vid,  to_vid  [, directed])
pgr_dijkstraCost(edges_sql, from_vid,  to_vids [, directed])
pgr_dijkstraCost(edges_sql, from_vids, to_vid  [, directed])
pgr_dijkstraCost(edges_sql, from_vids, to_vids [, directed])
pgr_dijkstraCost(edges_sql, combinations_sql   [, directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET


Using defaults

pgr_dijkstraCost(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_dijkstraCost(
'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_dijkstraCost(edges_sql, from_vid,  to_vid  [, directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Example :

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

SELECT * FROM pgr_dijkstraCost(
'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_dijkstraCost(edges_sql, from_vid,  to_vids [, directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Example :

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

SELECT * FROM pgr_dijkstraCost(
'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_dijkstraCost(edges_sql, from_vids, to_vid  [, directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Example :

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

SELECT * FROM pgr_dijkstraCost(
'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_dijkstraCost(edges_sql, from_vids, to_vids [, directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Example :

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

SELECT * FROM pgr_dijkstraCost(
'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_dijkstraCost(TEXT edges_sql, TEXT combination_sql, BOOLEAN directed:=true);
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Example :

Using a combinations table on an undirected graph

SELECT * FROM pgr_dijkstraCost(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
'SELECT source, target FROM combinations_table',
FALSE
);
start_vid  end_vid  agg_cost
-----------+---------+----------
1        2         1
1        4         3
2        1         1
2        4         2
(4 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 query

#### 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

### Return 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  .

Example 1 :

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

SELECT * FROM pgr_dijkstraCost(
'select id, source, target, cost, reverse_cost from edge_table',
ARRAY[5, 3, 4, 3, 3, 4], ARRAY[3, 5, 3, 4]);
start_vid  end_vid  agg_cost
-----------+---------+----------
3        4         3
3        5         2
4        3         1
4        5         3
5        3         4
5        4         3
(6 rows)


Example 2 :

Making start_vids the same as end_vids

SELECT * FROM pgr_dijkstraCost(
'select id, source, target, cost, reverse_cost from edge_table',
ARRAY[5, 3, 4], ARRAY[5, 3, 4]);
start_vid  end_vid  agg_cost
-----------+---------+----------
3        4         3
3        5         2
4        3         1
4        5         3
5        3         4
5        4         3
(6 rows)


Example 3 :

Four manually assigned (source, target) vertex combinations

SELECT * FROM pgr_dijkstraCost(
'SELECT id, source, target, cost FROM edge_table',
'SELECT * FROM (VALUES (2, 3), (2, 5), (11, 3), (11, 5)) AS combinations (source, target)',
FALSE
);
start_vid  end_vid  agg_cost
-----------+---------+----------
2        3         3
2        5         1
11        3         2
11        5         2
(4 rows)