## 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, from_vid,  to_vid  [, directed] [, driving_side])
pgr_withPointsCost(edges_sql, points_sql, from_vid,  to_vids [, directed] [, driving_side])
pgr_withPointsCost(edges_sql, points_sql, from_vids, to_vid  [, directed] [, driving_side])
pgr_withPointsCost(edges_sql, points_sql, from_vids, to_vids [, directed] [, driving_side])
pgr_withPointsCost(Edges SQL, Points SQL, Combinations SQL  [, directed] [, driving_side] [, details])
RETURNS SET OF (start_vid, end_vid, agg_cost)


Note

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

Using defaults

pgr_withPointsCost(edges_sql, points_sql, start_vid, end_vid)
RETURNS SET OF (start_vid, end_vid, agg_cost)

Example :

From point $$1$$ to point $$3$$

• For a directed graph.

• The driving side is set as b both. So arriving/departing to/from the point(s) can be in any direction.

SELECT * FROM pgr_withPointsCost(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
-1, -3);
start_pid  end_pid  agg_cost
-----------+---------+----------
-1       -3       3.2
(1 row)



#### One to One

pgr_withPointsCost(edges_sql, points_sql, from_vid,  to_vid  [, directed] [, driving_side])
RETURNS SET OF (seq, node, edge, cost, agg_cost)

Example :

From point $$1$$ to vertex $$3$$ on an undirected graph.

SELECT * FROM pgr_withPointsCost(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
-1, 3,
directed := false);
start_pid  end_pid  agg_cost
-----------+---------+----------
-1        3       1.6
(1 row)



#### One to Many

pgr_withPointsCost(edges_sql, points_sql, from_vid,  to_vids [, directed] [, driving_side])
RETURNS SET OF (start_vid, end_vid, agg_cost)

Example :

From point $$1$$ to point $$3$$ and vertex $$5$$ on a directed graph.

SELECT * FROM pgr_withPointsCost(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
-1, ARRAY[-3,5]);
start_pid  end_pid  agg_cost
-----------+---------+----------
-1       -3       3.2
-1        5       1.6
(2 rows)



#### Many to One

pgr_withPointsCost(edges_sql, points_sql, from_vids, to_vid  [, directed] [, driving_side])
RETURNS SET OF (start_vid, end_vid, agg_cost)

Example :

From point $$1$$ and vertex $$2$$ to point $$3$$ on a directed graph.

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



#### Many to Many

pgr_withPointsCost(edges_sql, points_sql, from_vids, to_vids [, directed] [, driving_side])
RETURNS SET OF (start_vid, end_vid, agg_cost)

Example :

From point $$1$$ and vertex $$2$$ to point $$3$$ and vertex $$7$$ on a directed graph.

SELECT * FROM pgr_withPointsCost(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[-1,2], ARRAY[-3,7]);
start_pid  end_pid  agg_cost
-----------+---------+----------
-1       -3       3.2
-1        7       3.6
2       -3       2.6
2        7         3
(4 rows)



#### Combinations SQL

pgr_withPointsCost(Edges SQL, Points SQL, Combinations SQL [, directed] [, driving_side] [, details])
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)

Example :

Two (source, target) combinations: (from point $$1$$ to vertex $$3$$ ), and (from vertex $$2$$ to point $$3$$ ) with right side driving topology.

SELECT * FROM pgr_withPointsCost(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
'SELECT * FROM ( VALUES (-1, 3), (2, -3) ) AS t(source, target)',
driving_side => 'r');
start_pid  end_pid  agg_cost
-----------+---------+----------
-1        3       6.4
2       -3       2.6
(2 rows)



### Parameters

Parameter

Type

Description

Edges SQL

 TEXT 

Edges query as described above.

Points SQL

 TEXT 

Points query as described above.

Combinations SQL

 TEXT 

Combinations query as described below.

start_vid

 ANY-INTEGER 

Starting vertex identifier. When negative: is a point’s pid.

end_vid

 ANY-INTEGER 

Ending vertex identifier. When negative: is a point’s pid.

start_vids

 ARRAY[ANY-INTEGER] 

Array of identifiers of starting vertices. When negative: is a point’s pid.

end_vids

 ARRAY[ANY-INTEGER] 

Array of identifiers of ending vertices. When negative: is a point’s pid.

directed

 BOOLEAN 

(optional). When  false  the graph is considered as Undirected. Default is  true  which considers the graph as Directed.

driving_side

 CHAR 

(optional) Value in [‘b’, ‘r’, ‘l’, NULL] indicating if the driving side is:
• In the right or left or

• If it doesn’t matter with ‘b’ or NULL.

• If column not present ‘b’ is considered.

### 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

#### Points query

Description of the Points SQL query

points_sql :

an SQL query, which should return a set of rows with the following columns:

Column

Type

Description

pid

 ANY-INTEGER 

(optional) Identifier of the point.

• If column present, it can not be NULL.

• If column not present, a sequential identifier 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 

(optional) Value in [‘b’, ‘r’, ‘l’, NULL] indicating if the point is:

• In the right, left of the edge or

• If it doesn’t matter with ‘b’ or NULL.

• If column not present ‘b’ is considered.

Where:

ANY-INTEGER :

smallint, int, bigint

ANY-NUMERICAL :

smallint, int, 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

### Result Columns

Column

Type

Description

start_vid

 BIGINT 

Identifier of the starting vertex. When negative: is a point’s pid.

end_vid

 BIGINT 

Identifier of the ending point. When negative: is a point’s pid.

agg_cost

 FLOAT 

Aggregate cost from  start_vid  to  end_vid  .

Example :

From point $$1$$ and vertex $$2$$ to point $$3$$ and vertex $$7$$ , with right side driving topology

SELECT * FROM pgr_withPointsCost(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[-1,2], ARRAY[-3,7],
driving_side := 'l');
start_pid  end_pid  agg_cost
-----------+---------+----------
-1       -3       3.2
-1        7       3.6
2       -3       2.6
2        7         3
(4 rows)


Example :

From point $$1$$ and vertex $$2$$ to point $$3$$ and vertex $$7$$ , with left side driving topology

SELECT * FROM pgr_withPointsCost(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[-1,2], ARRAY[-3,7],
driving_side := 'r');
start_pid  end_pid  agg_cost
-----------+---------+----------
-1       -3         4
-1        7       4.4
2       -3       2.6
2        7         3
(4 rows)


Example :

From point $$1$$ and vertex $$2$$ to point $$3$$ and vertex $$7$$ , does not matter driving side.

SELECT * FROM pgr_withPointsCost(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
ARRAY[-1,2], ARRAY[-3,7],
driving_side := 'b');
start_pid  end_pid  agg_cost
-----------+---------+----------
-1       -3       3.2
-1        7       3.6
2       -3       2.6
2        7         3
(4 rows)



The queries use the Sample Data network.