# 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 2.2.0
• New proposed function

Support

## 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])
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)



## Parameters¶

Parameter Type Description
edges_sql TEXT Edges SQL query as described above.
points_sql TEXT Points SQL query as described above.
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¶

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 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 smallint, int, bigint, real, float

## 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.