# 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

• New on v2.2.0

## 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])
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)



## Parameters¶

Parameter Type Default Description
edges_sql TEXT   Inner SQL query as described bellow.
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 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

## Return Columns¶

Returns set of (start_vid, end_vid, agg_cost)

Column Type Description
start_vid BIGINT Identifier of the starting vertex. Used when multiple starting vetrices are in the query.
end_vid BIGINT Identifier of the ending vertex. Used when multiple ending vertices are in the query.
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)