# pgr_withPointsKSP - Proposed¶

pgr_withPointsKSP - Find the K shortest paths using Yen’s algorithm.

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¶

Modifies the graph to include the points defined in the points_sql and using Yen algorithm, finds the $$K$$ shortest paths.

## Signatures¶

Summary

pgr_withPointsKSP(edges_sql, points_sql, start_pid, end_pid, K [, directed] [, heap_paths] [, driving_side] [, details])
RETURNS SET OF (seq, path_id, path_seq, node, edge, cost, agg_cost)


Using defaults

pgr_withPointsKSP(edges_sql, points_sql, start_pid, end_pid, K)
RETURNS SET OF (seq, path_id, path_seq, node, edge, cost, agg_cost)

Example: From point $$1$$ to point $$2$$ in $$2$$ cycles
• 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.
• No details are given about distance of other points of the query.
• No heap paths are returned.
SELECT * FROM pgr_withPointsKSP(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
-1, -2, 2);
seq | path_id | path_seq | node | edge | cost | agg_cost
-----+---------+----------+------+------+------+----------
1 |       1 |        1 |   -1 |    1 |  0.6 |        0
2 |       1 |        2 |    2 |    4 |    1 |      0.6
3 |       1 |        3 |    5 |    8 |    1 |      1.6
4 |       1 |        4 |    6 |    9 |    1 |      2.6
5 |       1 |        5 |    9 |   15 |  0.4 |      3.6
6 |       1 |        6 |   -2 |   -1 |    0 |        4
7 |       2 |        1 |   -1 |    1 |  0.6 |        0
8 |       2 |        2 |    2 |    4 |    1 |      0.6
9 |       2 |        3 |    5 |    8 |    1 |      1.6
10 |       2 |        4 |    6 |   11 |    1 |      2.6
11 |       2 |        5 |   11 |   13 |    1 |      3.6
12 |       2 |        6 |   12 |   15 |  0.6 |      4.6
13 |       2 |        7 |   -2 |   -1 |    0 |      5.2
(13 rows)



### Complete Signature¶

Finds the $$K$$ shortest paths depending on the optional parameters setup.

pgr_withPointsKSP(edges_sql, points_sql, start_pid, end_pid, K [, directed] [, heap_paths] [, driving_side] [, details])
RETURNS SET OF (seq, path_id, path_seq, node, edge, cost, agg_cost)

Example: From point $$1$$ to vertex $$6$$ in $$2$$ cycles with details.
SELECT * FROM pgr_withPointsKSP(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
-1, 6, 2, details := true);
seq | path_id | path_seq | node | edge | cost | agg_cost
-----+---------+----------+------+------+------+----------
1 |       1 |        1 |   -1 |    1 |  0.6 |        0
2 |       1 |        2 |    2 |    4 |  0.7 |      0.6
3 |       1 |        3 |   -6 |    4 |  0.3 |      1.3
4 |       1 |        4 |    5 |    8 |    1 |      1.6
5 |       1 |        5 |    6 |   -1 |    0 |      2.6
6 |       2 |        1 |   -1 |    1 |  0.6 |        0
7 |       2 |        2 |    2 |    4 |  0.7 |      0.6
8 |       2 |        3 |   -6 |    4 |  0.3 |      1.3
9 |       2 |        4 |    5 |   10 |    1 |      1.6
10 |       2 |        5 |   10 |   12 |  0.6 |      2.6
11 |       2 |        6 |   -3 |   12 |  0.4 |      3.2
12 |       2 |        7 |   11 |   13 |    1 |      3.6
13 |       2 |        8 |   12 |   15 |  0.6 |      4.6
14 |       2 |        9 |   -2 |   15 |  0.4 |      5.2
15 |       2 |       10 |    9 |    9 |    1 |      5.6
16 |       2 |       11 |    6 |   -1 |    0 |      6.6
(16 rows)



## Parameters¶

Parameter Type Description
edges_sql TEXT Edges SQL query as described above.
points_sql TEXT Points SQL query as described above.
start_pid ANY-INTEGER Starting point id.
end_pid ANY-INTEGER Ending point id.
K INTEGER Number of shortest paths.
directed BOOLEAN (optional). When false the graph is considered as Undirected. Default is true which considers the graph as Directed.
heap_paths BOOLEAN (optional). When true the paths calculated to get the shortests paths will be returned also. Default is false only the K shortest paths are returned.
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.
details BOOLEAN (optional). When true the results will include the driving distance to the points with in the distance. Default is false which ignores other points of the points_sql.

## 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
seq INTEGER Row sequence.
path_seq INTEGER Relative position in the path of node and edge. Has value 1 for the beginning of a path.
path_id INTEGER Path identifier. The ordering of the paths: For two paths i, j if i < j then agg_cost(i) <= agg_cost(j).
node BIGINT Identifier of the node in the path. Negative values are the identifiers of a point.
edge BIGINT
Identifier of the edge used to go from node to the next node in the path sequence.
• -1 for the last row in the path sequence.
cost FLOAT
Cost to traverse from node using edge to the next node in the path sequence.
• 0 for the last row in the path sequence.
agg_cost FLOAT
Aggregate cost from start_pid to node.
• 0 for the first row in the path sequence.

Example: Left side driving topology from point $$1$$ to point $$2$$ in $$2$$ cycles, with details
SELECT * FROM pgr_withPointsKSP(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
-1, -2, 2,
driving_side := 'l', details := true);
seq | path_id | path_seq | node | edge | cost | agg_cost
-----+---------+----------+------+------+------+----------
1 |       1 |        1 |   -1 |    1 |  0.6 |        0
2 |       1 |        2 |    2 |    4 |  0.7 |      0.6
3 |       1 |        3 |   -6 |    4 |  0.3 |      1.3
4 |       1 |        4 |    5 |    8 |    1 |      1.6
5 |       1 |        5 |    6 |    9 |    1 |      2.6
6 |       1 |        6 |    9 |   15 |    1 |      3.6
7 |       1 |        7 |   12 |   15 |  0.6 |      4.6
8 |       1 |        8 |   -2 |   -1 |    0 |      5.2
9 |       2 |        1 |   -1 |    1 |  0.6 |        0
10 |       2 |        2 |    2 |    4 |  0.7 |      0.6
11 |       2 |        3 |   -6 |    4 |  0.3 |      1.3
12 |       2 |        4 |    5 |    8 |    1 |      1.6
13 |       2 |        5 |    6 |   11 |    1 |      2.6
14 |       2 |        6 |   11 |   13 |    1 |      3.6
15 |       2 |        7 |   12 |   15 |  0.6 |      4.6
16 |       2 |        8 |   -2 |   -1 |    0 |      5.2
(16 rows)


Example: Right side driving topology from point $$1$$ to point $$2$$ in $$2$$ cycles, with heap paths and details
SELECT * FROM pgr_withPointsKSP(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
'SELECT pid, edge_id, fraction, side from pointsOfInterest',
-1, -2, 2,
heap_paths := true, driving_side := 'r', details := true);
seq | path_id | path_seq | node | edge | cost | agg_cost
-----+---------+----------+------+------+------+----------
1 |       1 |        1 |   -1 |    1 |  0.4 |        0
2 |       1 |        2 |    1 |    1 |    1 |      0.4
3 |       1 |        3 |    2 |    4 |  0.7 |      1.4
4 |       1 |        4 |   -6 |    4 |  0.3 |      2.1
5 |       1 |        5 |    5 |    8 |    1 |      2.4
6 |       1 |        6 |    6 |    9 |    1 |      3.4
7 |       1 |        7 |    9 |   15 |  0.4 |      4.4
8 |       1 |        8 |   -2 |   -1 |    0 |      4.8
9 |       2 |        1 |   -1 |    1 |  0.4 |        0
10 |       2 |        2 |    1 |    1 |    1 |      0.4
11 |       2 |        3 |    2 |    4 |  0.7 |      1.4
12 |       2 |        4 |   -6 |    4 |  0.3 |      2.1
13 |       2 |        5 |    5 |    8 |    1 |      2.4
14 |       2 |        6 |    6 |   11 |    1 |      3.4
15 |       2 |        7 |   11 |   13 |    1 |      4.4
16 |       2 |        8 |   12 |   15 |    1 |      5.4
17 |       2 |        9 |    9 |   15 |  0.4 |      6.4
18 |       2 |       10 |   -2 |   -1 |    0 |      6.8
19 |       3 |        1 |   -1 |    1 |  0.4 |        0
20 |       3 |        2 |    1 |    1 |    1 |      0.4
21 |       3 |        3 |    2 |    4 |  0.7 |      1.4
22 |       3 |        4 |   -6 |    4 |  0.3 |      2.1
23 |       3 |        5 |    5 |   10 |    1 |      2.4
24 |       3 |        6 |   10 |   12 |  0.6 |      3.4
25 |       3 |        7 |   -3 |   12 |  0.4 |        4
26 |       3 |        8 |   11 |   13 |    1 |      4.4
27 |       3 |        9 |   12 |   15 |    1 |      5.4
28 |       3 |       10 |    9 |   15 |  0.4 |      6.4
29 |       3 |       11 |   -2 |   -1 |    0 |      6.8
(29 rows)



The queries use the Sample Data network.