# 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.

Boost Graph Inside

Availability

• Version 3.1.0

• New Proposed functions:

• pgr_dijkstraCost(combinations)

• Version 2.2.0

• New Official function

• Supported versions: current(3.1) 3.0 2.6

• Unsupported versions: 2.5 2.4 2.3 2.3

## 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]) -- Proposed on v3.1
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.

## Additional Examples¶

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)



## See Also¶

Indices and tables