# pgr_bdDijkstraCostMatrix¶

pgr_bdDijkstraCostMatrix - Calculates a cost matrix using pgr_bdDijkstra.

Availability

• Version 3.0.0

• Official function

• Version 2.5.0

• New proposed function

## Description¶

Using bidirectional Dijkstra algorithm, calculate and return a cost matrix.

• 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 (worse case scenario): $$O((V \log V + E))$$

• For large graphs where there is a path bewtween the starting vertex and ending vertex:

• It is expected to terminate faster than pgr_dijkstra

The main Characteristics are:

• Can be used as input to pgr_TSP.

• Use directly when the resulting matrix is symmetric and there is no $$\infty$$ value.

• It will be the users responsibility to make the matrix symmetric.

• By using geometric or harmonic average of the non symmetric values.

• By using max or min the non symmetric values.

• By setting the upper triangle to be the mirror image of the lower triangle.

• By setting the lower triangle to be the mirror image of the upper triangle.

• It is also the users responsibility to fix an $$\infty$$ value.

• Each function works as part of the family it belongs to.

• 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.

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

• The aggregate cost in 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 in the non included values (u, v) is $$\infty$$.

• Let be the case the values returned are stored in a table:

• 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 vids are ignored.

• The returned values are ordered:

• start_vid ascending

• end_vid ascending

## Signatures¶

Summary

pgr_bdDijkstraCostMatrix(Edges SQL, start vids, [directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET
Example:

Symmetric cost matrix for vertices $$\{5, 6, 10, 15\}$$ on an undirected graph

SELECT * FROM pgr_bdDijkstraCostMatrix(
'SELECT id, source, target, cost, reverse_cost FROM edges',
(SELECT array_agg(id)
FROM vertices
WHERE id IN (5, 6, 10, 15)),
false);
start_vid | end_vid | agg_cost
-----------+---------+----------
5 |       6 |        1
5 |      10 |        2
5 |      15 |        3
6 |       5 |        1
6 |      10 |        1
6 |      15 |        2
10 |       5 |        2
10 |       6 |        1
10 |      15 |        1
15 |       5 |        3
15 |       6 |        2
15 |      10 |        1
(12 rows)



## Parameters¶

Column

Type

Description

Edges SQL

TEXT

Edges SQL as described below

start vids

ARRAY[BIGINT]

Array of identifiers of starting 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

## 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:

Use with pgr_TSP.

SELECT * FROM pgr_TSP(
$$SELECT * FROM pgr_bdDijkstraCostMatrix( 'SELECT id, source, target, cost, reverse_cost FROM edges', (SELECT array_agg(id) FROM vertices WHERE id IN (5, 6, 10, 15)), false)$$);
NOTICE:  pgr_TSP no longer solving with simulated annaeling
HINT:  Ignoring annaeling parameters
seq | node | cost | agg_cost
-----+------+------+----------
1 |    5 |    0 |        0
2 |    6 |    1 |        1
3 |   10 |    1 |        2
4 |   15 |    1 |        3
5 |    5 |    3 |        6
(5 rows)