# pgr_withPointsKSP - Proposed¶

pgr_withPointsKSP — Yen’s algorithm for K shortest paths using Dijkstra.

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

## Description¶

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

## Signatures¶

pgr_withPointsKSP(Edges SQL, Points SQL start vid, end vid, K, [options])
options: [directed, heap_paths, driving_side, details]
RETURNS SET OF (seq, path_id, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET
Example:

Get 2 paths from Point $$1$$ to point $$2$$ on a directed graph.

• 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 edges 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 |    6 |    4 |    1 |      0.6
3 |       1 |        3 |    7 |    8 |    1 |      1.6
4 |       1 |        4 |   11 |    9 |    1 |      2.6
5 |       1 |        5 |   16 |   15 |  0.4 |      3.6
6 |       1 |        6 |   -2 |   -1 |    0 |        4
7 |       2 |        1 |   -1 |    1 |  0.6 |        0
8 |       2 |        2 |    6 |    4 |    1 |      0.6
9 |       2 |        3 |    7 |    8 |    1 |      1.6
10 |       2 |        4 |   11 |   11 |    1 |      2.6
11 |       2 |        5 |   12 |   13 |    1 |      3.6
12 |       2 |        6 |   17 |   15 |  0.6 |      4.6
13 |       2 |        7 |   -2 |   -1 |    0 |      5.2
(13 rows)



## Parameters¶

Column

Type

Description

Edges SQL

TEXT

Edges SQL query as described.

Points SQL

TEXT

Points SQL query as described.

start vid

ANY-INTEGER

Identifier of the departure vertex.

• Negative values represent a point

end vid

ANY-INTEGER

Identifier of the destination vertex.

• Negative values represent a point

K

ANY-INTEGER

Number of required paths

Where:

ANY-INTEGER:

SMALLINT, INTEGER, BIGINT

### Optional parameters¶

Column

Type

Default

Description

directed

BOOLEAN

true

• When true the graph is considered Directed

• When false the graph is considered as Undirected.

## KSP Optional parameters¶

Column

Type

Default

Description

heap_paths

BOOLEAN

false

• When false Returns at most K paths.

• When true all the calculated paths while processing are returned.

• Roughly, when the shortest path has N edges, the heap will contain about than N * K paths for small value of K and K > 5.

### 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.

details

BOOLEAN

false

• When true the results will include the points that are in the path.

• When false the results will not include the points that are in the path.

## 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

## Result Columns¶

Returns set of (seq, path_id, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)

Column

Type

Description

seq

INTEGER

Sequential value starting from 1.

path_id

INTEGER

Path identifier.

• Has value 1 for the first of a path from start vid to end_vid

path_seq

INTEGER

Relative position in the path. Has value 1 for the beginning of a path.

node

BIGINT

Identifier of the node in the path from start vid to end vid

edge

BIGINT

Identifier of the edge used to go from node to the next node in the path sequence. -1 for the last node of the path.

cost

FLOAT

Cost to traverse from node using edge to the next node in the path sequence.

• $$0$$ for the last node of the path.

agg_cost

FLOAT

Aggregate cost from start vid to node.

### Use pgr_findCloseEdges in the Points SQL.¶

Get $$2$$ paths using left side driving topology, from vertex $$1$$ to the closest location on the graph of point (2.9, 1.8).

SELECT * FROM pgr_withPointsKSP(
$e$ 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, -1, 2,
driving_side := 'r');
seq | path_id | path_seq | node | edge | cost | agg_cost
-----+---------+----------+------+------+------+----------
1 |       1 |        1 |    1 |    6 |    1 |        0
2 |       1 |        2 |    3 |    7 |    1 |        1
3 |       1 |        3 |    7 |    8 |    1 |        2
4 |       1 |        4 |   11 |    9 |    1 |        3
5 |       1 |        5 |   16 |   16 |    1 |        4
6 |       1 |        6 |   15 |    3 |    1 |        5
7 |       1 |        7 |   10 |    5 |  0.8 |        6
8 |       1 |        8 |   -1 |   -1 |    0 |      6.8
9 |       2 |        1 |    1 |    6 |    1 |        0
10 |       2 |        2 |    3 |    7 |    1 |        1
11 |       2 |        3 |    7 |   10 |    1 |        2
12 |       2 |        4 |    8 |   12 |    1 |        3
13 |       2 |        5 |   12 |   13 |    1 |        4
14 |       2 |        6 |   17 |   15 |    1 |        5
15 |       2 |        7 |   16 |   16 |    1 |        6
16 |       2 |        8 |   15 |    3 |    1 |        7
17 |       2 |        9 |   10 |    5 |  0.8 |        8
18 |       2 |       10 |   -1 |   -1 |    0 |      8.8
(18 rows)


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

### Left driving side¶

Get $$2$$ paths using left side driving topology, from point $$1$$ to point $$2$$ with details.

SELECT * FROM pgr_withPointsKSP(
'SELECT id, source, target, cost, reverse_cost FROM edges 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 |    6 |    4 |  0.7 |      0.6
3 |       1 |        3 |   -6 |    4 |  0.3 |      1.3
4 |       1 |        4 |    7 |    8 |    1 |      1.6
5 |       1 |        5 |   11 |   11 |    1 |      2.6
6 |       1 |        6 |   12 |   13 |    1 |      3.6
7 |       1 |        7 |   17 |   15 |  0.6 |      4.6
8 |       1 |        8 |   -2 |   -1 |    0 |      5.2
9 |       2 |        1 |   -1 |    1 |  0.6 |        0
10 |       2 |        2 |    6 |    4 |  0.7 |      0.6
11 |       2 |        3 |   -6 |    4 |  0.3 |      1.3
12 |       2 |        4 |    7 |    8 |    1 |      1.6
13 |       2 |        5 |   11 |    9 |    1 |      2.6
14 |       2 |        6 |   16 |   15 |    1 |      3.6
15 |       2 |        7 |   17 |   15 |  0.6 |      4.6
16 |       2 |        8 |   -2 |   -1 |    0 |      5.2
(16 rows)



### Right driving side¶

Get $$2$$ paths using right side driving topology from, point $$1$$ to point $$2$$ with heap paths and details.

SELECT * FROM pgr_withPointsKSP(
'SELECT id, source, target, cost, reverse_cost FROM edges 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 |    5 |    1 |    1 |      0.4
3 |       1 |        3 |    6 |    4 |  0.7 |      1.4
4 |       1 |        4 |   -6 |    4 |  0.3 |      2.1
5 |       1 |        5 |    7 |    8 |    1 |      2.4
6 |       1 |        6 |   11 |    9 |    1 |      3.4
7 |       1 |        7 |   16 |   15 |  0.4 |      4.4
8 |       1 |        8 |   -2 |   -1 |    0 |      4.8
9 |       2 |        1 |   -1 |    1 |  0.4 |        0
10 |       2 |        2 |    5 |    1 |    1 |      0.4
11 |       2 |        3 |    6 |    4 |  0.7 |      1.4
12 |       2 |        4 |   -6 |    4 |  0.3 |      2.1
13 |       2 |        5 |    7 |    8 |    1 |      2.4
14 |       2 |        6 |   11 |   11 |    1 |      3.4
15 |       2 |        7 |   12 |   13 |    1 |      4.4
16 |       2 |        8 |   17 |   15 |    1 |      5.4
17 |       2 |        9 |   16 |   15 |  0.4 |      6.4
18 |       2 |       10 |   -2 |   -1 |    0 |      6.8
19 |       3 |        1 |   -1 |    1 |  0.4 |        0
20 |       3 |        2 |    5 |    1 |    1 |      0.4
21 |       3 |        3 |    6 |    4 |  0.7 |      1.4
22 |       3 |        4 |   -6 |    4 |  0.3 |      2.1
23 |       3 |        5 |    7 |   10 |    1 |      2.4
24 |       3 |        6 |    8 |   12 |  0.6 |      3.4
25 |       3 |        7 |   -3 |   12 |  0.4 |        4
26 |       3 |        8 |   12 |   13 |    1 |      4.4
27 |       3 |        9 |   17 |   15 |    1 |      5.4
28 |       3 |       10 |   16 |   15 |  0.4 |      6.4
29 |       3 |       11 |   -2 |   -1 |    0 |      6.8
(29 rows)



The queries use the Sample Data network.