# pgr_dijkstraCost¶

## Synopsis¶

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.

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.

## Characteristics¶

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

## Signature Summary¶

pgr_dijkstraCost(edges_sql, start_vid, end_vid);
pgr_dijkstraCost(edges_sql, start_vid, end_vid, directed);
pgr_dijkstraCost(edges_sql, start_vids, end_vid, directed);
pgr_dijkstraCost(edges_sql, start_vid, end_vids, directed);
pgr_dijkstraCost(edges_sql, start_vids, end_vids, directed);

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


## Signatures¶

### Minimal signature¶

The minimal signature is for a directed graph from one start_vid to one end_vid:

pgr_dijkstraCost(TEXT edges_sql, BIGINT start_vid, BIGINT end_vid)
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET


Example

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)


### pgr_dijkstraCost One to One¶

This signature performs a Dijkstra from one start_vid to one end_vid:
• on a directed graph when directed flag is missing or is set to true.
• on an undirected graph when directed flag is set to false.
pgr_dijkstraCost(TEXT edges_sql, BIGINT start_vid, BIGINT end_vid,
BOOLEAN directed:=true);
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET

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)


### pgr_dijkstraCost One to Many¶

pgr_dijkstraCost(TEXT edges_sql, BIGINT start_vid, array[ANY_INTEGER] end_vids,
BOOLEAN directed:=true);
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET

This signature performs a Dijkstra from one start_vid to each end_vid in end_vids:
• on a directed graph when directed flag is missing or is set to true.
• on an undirected graph when directed flag is set to false.
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)


### pgr_dijkstraCost Many to One¶

pgr_dijkstraCost(TEXT edges_sql, array[ANY_INTEGER] start_vids, BIGINT end_vid,
BOOLEAN directed:=true);
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET

This signature performs a Dijkstra from each start_vid in start_vids to one end_vid:
• on a directed graph when directed flag is missing or is set to true.
• on an undirected graph when directed flag is set to false.
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)


### pgr_dijkstraCost Many to Many¶

pgr_dijkstraCost(TEXT edges_sql, array[ANY_INTEGER] start_vids, array[ANY_INTEGER] end_vids,
BOOLEAN directed:=true);
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET

This signature performs a Dijkstra from each start_vid in start_vids to each end_vid in end_vids:
• on a directed graph when directed flag is missing or is set to true.
• on an undirected graph when directed flag is set to false.
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)


## Description of the Signatures¶

### Description of the edges_sql query¶

edges_sql: an SQL query, which should return a set of rows with the following columns:
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 SMALLINT, INTEGER, BIGINT, REAL, FLOAT

### Description of the parameters of the signatures¶

Column Type Default Description
sql TEXT   SQL query as described above.
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.

### Description of the return values¶

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 of the shortest path 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)


History

• New in version 2.2.0