# pgr_dijkstraCost¶

pgr_dijkstraCost - Total cost of the shortest path(s) using Dijkstra algorithm.

Availability

• Version 3.1.0

• New proposed signature:

• Version 2.2.0

• New Official function

## Description¶

The pgr_dijkstraCost function sumarizes of the cost of the shortest path(s) using Dijkstra Algorithm.

Dijkstra’s algorithm, conceived by Dutch computer scientist Edsger Dijkstra in 1956. It is a graph search algorithm that solves the shortest path problem for a graph with non-negative edge path costs, producing a shortest path from a starting vertex to an ending vertex. This implementation can be used with a directed graph and an undirected graph.

• 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: $$O(| start\ vids | * (V \log V + E))$$

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

### One to One¶

pgr_dijkstraCost(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_dijkstraCost(
'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_dijkstraCost(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_dijkstraCost(
'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_dijkstraCost(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_dijkstraCost(
'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_dijkstraCost(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_dijkstraCost(
'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_dijkstraCost(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_dijkstraCost(
'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

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.

## 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_dijkstraCost(
'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_dijkstraCost(
'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_dijkstraCost(
'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)