# pgr_withPointsCost - Proposed¶

pgr_withPointsCost - Calculates the shortest path and returns only the aggregate cost of the shortest path(s) found, for the combination of points given.

Warning

Proposed functions for next mayor release.

• They are not officially in the current release.

• They will likely officially be part of the next mayor release:

• The functions make use of ANY-INTEGER and ANY-NUMERICAL

• Name might not change. (But still can)

• Signature might not change. (But still can)

• Functionality might not change. (But still can)

• pgTap tests have being done. But might need more.

• Documentation might need refinement.

Availability

• Version 3.2.0

• New proposed function:

• pgr_withPointsCost(Combinations)

• Version 2.2.0

• New proposed function

## Description¶

Modify the graph to include points defined by points_sql. Using Dijkstra algorithm, return only the aggregate cost of the shortest path(s) found.

The main characteristics are:
• It does not return a path.

• Returns the sum of the costs of the shortest path for pair combination of vertices in the modified graph.

• Vertices of the graph are:

• positive when it belongs to the edges_sql

• negative when it belongs to the points_sql

• 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 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 agg_cost in the non included values (u, v) is $$\infty$$

• If the values returned are stored in a table, 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).

• For optimization purposes, 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_withPointsCost(Edges SQL, ‘Points SQL_, start vid, end vid, [options])
pgr_withPointsCost(Edges SQL, ‘Points SQL_, start vid, end vids, [options])
pgr_withPointsCost(Edges SQL, ‘Points SQL_, start vids, end vid, [options])
pgr_withPointsCost(Edges SQL, ‘Points SQL_, start vids, end vids, [options])
pgr_withPointsCost(Edges SQL, ‘Points SQL_, Combinations SQL, [options])
options: [directed, driving_side]
RETURNS SET OF (start_pid, end_pid, agg_cost)
OR EMPTY SET

Note

There is no details flag, unlike the other members of the withPoints family of functions.

### One to One¶

pgr_withPointsCost(Edges SQL, ‘Points SQL_, start vid, end vid, [options])
options: [directed, driving_side]
RETURNS SET OF (start_pid, end_pid, agg_cost)
OR EMPTY SET
Example:

From point $$1$$ to vertex $$10$$ with defaults

SELECT * FROM pgr_withPointsCost(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
-1, 10);
start_pid | end_pid | agg_cost
-----------+---------+----------
-1 |      10 |      5.6
(1 row)



### One to Many¶

pgr_withPointsCost(Edges SQL, Points SQL, start vid, end vids, [options])
options: [directed, driving_side]
RETURNS SET OF (start_pid, end_pid, agg_cost)
OR EMPTY SET
Example:

From point $$1$$ to point $$3$$ and vertex $$7$$ on an undirected graph

SELECT * FROM pgr_withPointsCost(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
-1, ARRAY[-3, 7],
directed => false);
start_pid | end_pid | agg_cost
-----------+---------+----------
-1 |      -3 |      3.2
-1 |       7 |      1.6
(2 rows)



### Many to One¶

pgr_withPointsCost(Edges SQL, Points SQL, start vids, end vid, [options])
options: [directed, driving_side]
RETURNS SET OF (start_pid, end_pid, agg_cost)
OR EMPTY SET
Example:

From point $$1$$ and vertex $$6$$ to point $$3$$

SELECT * FROM pgr_withPointsCost(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[-1, 6], -3);
start_pid | end_pid | agg_cost
-----------+---------+----------
-1 |      -3 |      3.2
6 |      -3 |      2.6
(2 rows)



### Many to Many¶

pgr_withPointsCost(Edges SQL, Points SQL, start vids, end vids, [options])
options: [directed, driving_side]
RETURNS SET OF (start_pid, end_pid, agg_cost)
OR EMPTY SET
Example:

From point $$15$$ and vertex $$6$$ to point $$3$$ and vertex $$1$$

SELECT * FROM pgr_withPointsCost(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[-1, 6], ARRAY[-3, 1]);
start_pid | end_pid | agg_cost
-----------+---------+----------
-1 |      -3 |      3.2
-1 |       1 |      3.6
6 |      -3 |      2.6
6 |       1 |        3
(4 rows)



### Combinations¶

pgr_withPointsCost(Edges SQL, Points SQL, Combinations SQL, [options])
options: [directed, driving_side]
RETURNS SET OF (start_pid, end_pid, agg_cost)
OR EMPTY SET
Example:

Two combinations

From point $$1$$ to vertex $$10$$, and from vertex $$6$$ to point $$3$$ with right side driving.

SELECT * FROM pgr_withPointsCost(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
'SELECT * FROM (VALUES (-1, 10), (6, -3)) AS combinations(source, target)',
driving_side => 'r');
start_pid | end_pid | agg_cost
-----------+---------+----------
-1 |      10 |      6.4
6 |      -3 |      2.6
(2 rows)



## Parameters¶

Column

Type

Description

Edges SQL

TEXT

Edges SQL as described below

Points SQL

TEXT

Points SQL as described below

Combinations SQL

TEXT

Combinations SQL as described below

start vid

BIGINT

Identifier of the starting vertex of the path. Negative value is for point’s identifier.

start vids

ARRAY[BIGINT]

Array of identifiers of starting vertices. Negative values are for point’s identifiers.

end vid

BIGINT

Identifier of the ending vertex of the path. Negative value is for point’s identifier.

end vids

ARRAY[BIGINT]

Array of identifiers of ending vertices. Negative values are for point’s identifiers.

### Optional parameters¶

Column

Type

Default

Description

directed

BOOLEAN

true

• When true the graph is considered Directed

• When false the graph is considered as Undirected.

### With points optional parameters¶

Parameter

Type

Default

Description

driving_side

CHAR

b

Value in [r, l, b] indicating if the driving side is:

• r for right driving side.

• l for left driving side.

• b for both.

## 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

### Points SQL¶

Parameter

Type

Default

Description

pid

ANY-INTEGER

value

Identifier of the point.

• Use with positive value, as internally will be converted to negative value

• If column is present, it can not be NULL.

• If column is not present, a sequential negative value will be given automatically.

edge_id

ANY-INTEGER

Identifier of the “closest” edge to the point.

fraction

ANY-NUMERICAL

Value in <0,1> that indicates the relative postition from the first end point of the edge.

side

CHAR

b

Value in [b, r, l, NULL] indicating if the point is:

• In the right r,

• In the left l,

• In both sides b, NULL

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¶

Column

Type

Description

start_pid

BIGINT

Identifier of the starting vertex or point.

• When positive: is a vertex’s identifier.

• When negative: is a point’s identifier.

end_pid

BIGINT

Identifier of the ending vertex or point.

• When positive: is a vertex’s identifier.

• When negative: is a point’s identifier.

agg_cost

FLOAT

Aggregate cost from start_vid to end_vid.

### Use pgr_findCloseEdges in the Points SQL.¶

Find the cost of the routes from vertex $$1$$ to the two closest locations on the graph of point (2.9, 1.8).

SELECT * FROM pgr_withPointsCost(
$e$ SELECT * FROM edges $e$,
$p$ SELECT edge_id, round(fraction::numeric, 2) AS fraction, side
FROM pgr_findCloseEdges(
$$SELECT id, geom FROM edges$$,
(SELECT ST_POINT(2.9, 1.8)),
0.5, cap => 2)
$p$,
1, ARRAY[-1, -2]);
start_pid | end_pid | agg_cost
-----------+---------+----------
1 |      -2 |      2.9
1 |      -1 |      6.8
(2 rows)


• Point $$-1$$ corresponds to the closest edge from point (2.9,1.8).

• Point $$-2$$ corresponds to the next close edge from point (2.9,1.8).

• Being close to the graph does not mean have a shorter route.

### Right side driving topology¶

Traveling from point $$1$$ and vertex $$5$$ to points $$\{2, 3, 6\}$$ and vertices $$\{10, 11\}$$

SELECT * FROM pgr_withPointsCost(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[5, -1], ARRAY[-2, -3, -6, 10, 11],
driving_side => 'r');
start_pid | end_pid | agg_cost
-----------+---------+----------
-1 |      -6 |      2.1
-1 |      -3 |        4
-1 |      -2 |      4.8
-1 |      10 |      6.4
-1 |      11 |      3.4
5 |      -6 |      1.7
5 |      -3 |      3.6
5 |      -2 |      4.4
5 |      10 |        6
5 |      11 |        3
(10 rows)



### Left side driving topology¶

Traveling from point $$1$$ and vertex $$5$$ to points $$\{2, 3, 6\}$$ and vertices $$\{10, 11\}$$

SELECT * FROM pgr_withPointsCost(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[5, -1], ARRAY[-2, -3, -6, 10, 11],
driving_side => 'l');
start_pid | end_pid | agg_cost
-----------+---------+----------
-1 |      -6 |      1.3
-1 |      -3 |      3.2
-1 |      -2 |      5.2
-1 |      10 |      5.6
-1 |      11 |      2.6
5 |      -6 |      1.7
5 |      -3 |      3.6
5 |      -2 |      5.6
5 |      10 |        6
5 |      11 |        3
(10 rows)



### Does not matter driving side driving topology¶

Traveling from point $$1$$ and vertex $$5$$ to points $$\{2, 3, 6\}$$ and vertices $$\{10, 11\}$$

SELECT * FROM pgr_withPointsCost(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[5, -1], ARRAY[-2, -3, -6, 10, 11]);
start_pid | end_pid | agg_cost
-----------+---------+----------
-1 |      -6 |      1.3
-1 |      -3 |      3.2
-1 |      -2 |        4
-1 |      10 |      5.6
-1 |      11 |      2.6
5 |      -6 |      1.7
5 |      -3 |      3.6
5 |      -2 |      4.4
5 |      10 |        6
5 |      11 |        3
(10 rows)



The queries use the Sample Data network.