# pgr_KSP¶

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

Availability

• Version 2.1.0

• Signature change

• Old signature no longer supported

• Version 2.0.0

• Official function

## Description¶

The K shortest path routing algorithm based on Yen’s algorithm. “K” is the number of shortest paths desired.

## Signatures¶

Summary

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

Get 2 paths from $$6$$ to $$17$$ on a directed graph.

SELECT * FROM pgr_KSP(
'SELECT id, source, target, cost, reverse_cost FROM edges',
6, 17, 2);
seq | path_id | path_seq | node | edge | cost | agg_cost
-----+---------+----------+------+------+------+----------
1 |       1 |        1 |    6 |    4 |    1 |        0
2 |       1 |        2 |    7 |   10 |    1 |        1
3 |       1 |        3 |    8 |   12 |    1 |        2
4 |       1 |        4 |   12 |   13 |    1 |        3
5 |       1 |        5 |   17 |   -1 |    0 |        4
6 |       2 |        1 |    6 |    4 |    1 |        0
7 |       2 |        2 |    7 |    8 |    1 |        1
8 |       2 |        3 |   11 |    9 |    1 |        2
9 |       2 |        4 |   16 |   15 |    1 |        3
10 |       2 |        5 |   17 |   -1 |    0 |        4
(10 rows)



## Parameters¶

Column

Type

Description

Edges SQL

TEXT

SQL query as described.

start vid

ANY-INTEGER

Identifier of the departure vertex.

end vid

ANY-INTEGER

Identifier of the arrival vertex.

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.

## 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

## 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.

Example:

Get 2 paths from $$6$$ to $$17$$ on an undirected graph

Also get the paths in the heap.

SELECT * FROM pgr_KSP(
'SELECT id, source, target, cost, reverse_cost FROM edges',
6, 17, 2,
directed => false, heap_paths => true
);
seq | path_id | path_seq | node | edge | cost | agg_cost
-----+---------+----------+------+------+------+----------
1 |       1 |        1 |    6 |    4 |    1 |        0
2 |       1 |        2 |    7 |   10 |    1 |        1
3 |       1 |        3 |    8 |   12 |    1 |        2
4 |       1 |        4 |   12 |   13 |    1 |        3
5 |       1 |        5 |   17 |   -1 |    0 |        4
6 |       2 |        1 |    6 |    4 |    1 |        0
7 |       2 |        2 |    7 |    8 |    1 |        1
8 |       2 |        3 |   11 |   11 |    1 |        2
9 |       2 |        4 |   12 |   13 |    1 |        3
10 |       2 |        5 |   17 |   -1 |    0 |        4
11 |       3 |        1 |    6 |    4 |    1 |        0
12 |       3 |        2 |    7 |    8 |    1 |        1
13 |       3 |        3 |   11 |    9 |    1 |        2
14 |       3 |        4 |   16 |   15 |    1 |        3
15 |       3 |        5 |   17 |   -1 |    0 |        4
16 |       4 |        1 |    6 |    2 |    1 |        0
17 |       4 |        2 |   10 |    5 |    1 |        1
18 |       4 |        3 |   11 |    9 |    1 |        2
19 |       4 |        4 |   16 |   15 |    1 |        3
20 |       4 |        5 |   17 |   -1 |    0 |        4
(20 rows)