# pgRouting Manual (3.0-rc1)

## pgr_KSP

`pgr_KSP` — Returns the “K” shortest paths.

Boost Graph Inside

Availability

- Version 2.1.0
  - Signature change
    - Old signature no longer supported
- Version 2.0.0
  - Official function

Support

- Supported versions: current(3.0) 2.6
- Unsupported versions: 2.5 2.4 2.3 2.2 2.1 2.0

## 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 [, directed] [, heap_paths])
    RETURNS SET OF (seq, path_id, path_seq, node, edge, cost, agg_cost) or EMPTY SET

Using defaults

    pgr_ksp(edges_sql, start_vid, end_vid, K);
    RETURNS SET OF (seq, path_id, path_seq, node, edge, cost, agg_cost) or EMPTY SET

Example: | TBD

### Complete Signature

    pgr_KSP(edges_sql, start_vid, end_vid, K [, directed] [, heap_paths])
    RETURNS SET OF (seq, path_id, path_seq, node, edge, cost, agg_cost) or EMPTY SET

Example: | TBD

## Parameters

Column | Type | Description
--- | --- | ---
edges_sql | `TEXT` | SQL query as described above.
start_vid | `BIGINT` | Identifier of the starting vertex.
end_vid | `BIGINT` | Identifier of the ending vertex.
k | `INTEGER` | The desiered number of 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` returns all the paths stored in the process heap. Default is `false` which only returns `k` paths.

Roughly, if the shortest path has `N` edges, the heap will contain about than `N * k` paths for small value of `k` and `k > 1`.

## 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
ANY-NUMERICAL: | SMALLINT, INTEGER, BIGINT, REAL, FLOAT

## Result Columns

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

Column | Type | Description
--- | --- | ---
seq | `INTEGER` | Sequential value starting from 1.
path_seq | `INTEGER` | Relative position in the path of `node` and `edge`. Has value 1 for the beginning of a path.
path_id | `BIGINT` | 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.
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 route.
cost | `FLOAT` | Cost to traverse from `node` using `edge` to the next node in the path sequence.
agg_cost | `FLOAT` | Aggregate cost from `start_vid` to `node`.

## Additional Examples

Example: | To handle the one flag to choose signatures

The examples in this section use the following Network for queries marked as directed and cost and reverse_cost columns are used

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

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

Example: | For queries marked as `directed` with `cost` and `reverse_cost` columns

The examples in this section use the following Network for queries marked as directed and cost and reverse_cost columns are used

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

    SELECT * FROM pgr_KSP(
         'SELECT id, source, target, cost, reverse_cost FROM edge_table',
          2, 12, 2, heap_paths:=true
       );
     seq | path_id | path_seq | node | edge | cost | agg_cost
    -----+---------+----------+------+------+------+----------
       1 |       1 |        1 |    2 |    4 |    1 |        0
       2 |       1 |        2 |    5 |    8 |    1 |        1
       3 |       1 |        3 |    6 |    9 |    1 |        2
       4 |       1 |        4 |    9 |   15 |    1 |        3
       5 |       1 |        5 |   12 |   -1 |    0 |        4
       6 |       2 |        1 |    2 |    4 |    1 |        0
       7 |       2 |        2 |    5 |    8 |    1 |        1
       8 |       2 |        3 |    6 |   11 |    1 |        2
       9 |       2 |        4 |   11 |   13 |    1 |        3
      10 |       2 |        5 |   12 |   -1 |    0 |        4
      11 |       3 |        1 |    2 |    4 |    1 |        0
      12 |       3 |        2 |    5 |   10 |    1 |        1
      13 |       3 |        3 |   10 |   12 |    1 |        2
      14 |       3 |        4 |   11 |   13 |    1 |        3
      15 |       3 |        5 |   12 |   -1 |    0 |        4
    (15 rows)

    SELECT * FROM pgr_KSP(
         'SELECT id, source, target, cost, reverse_cost FROM edge_table',
          2, 12, 2, true, true
       );
     seq | path_id | path_seq | node | edge | cost | agg_cost
    -----+---------+----------+------+------+------+----------
       1 |       1 |        1 |    2 |    4 |    1 |        0
       2 |       1 |        2 |    5 |    8 |    1 |        1
       3 |       1 |        3 |    6 |    9 |    1 |        2
       4 |       1 |        4 |    9 |   15 |    1 |        3
       5 |       1 |        5 |   12 |   -1 |    0 |        4
       6 |       2 |        1 |    2 |    4 |    1 |        0
       7 |       2 |        2 |    5 |    8 |    1 |        1
       8 |       2 |        3 |    6 |   11 |    1 |        2
       9 |       2 |        4 |   11 |   13 |    1 |        3
      10 |       2 |        5 |   12 |   -1 |    0 |        4
      11 |       3 |        1 |    2 |    4 |    1 |        0
      12 |       3 |        2 |    5 |   10 |    1 |        1
      13 |       3 |        3 |   10 |   12 |    1 |        2
      14 |       3 |        4 |   11 |   13 |    1 |        3
      15 |       3 |        5 |   12 |   -1 |    0 |        4
    (15 rows)

Examples: | For queries marked as `undirected` with `cost` and `reverse_cost` columns

The examples in this section use the following Network for queries marked as undirected and cost and reverse_cost columns are used

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

    SELECT * FROM pgr_KSP(
         'SELECT id, source, target, cost, reverse_cost FROM edge_table',
          2, 12, 2, false, true
       );
     seq | path_id | path_seq | node | edge | cost | agg_cost
    -----+---------+----------+------+------+------+----------
       1 |       1 |        1 |    2 |    2 |    1 |        0
       2 |       1 |        2 |    3 |    3 |    1 |        1
       3 |       1 |        3 |    4 |   16 |    1 |        2
       4 |       1 |        4 |    9 |   15 |    1 |        3
       5 |       1 |        5 |   12 |   -1 |    0 |        4
       6 |       2 |        1 |    2 |    4 |    1 |        0
       7 |       2 |        2 |    5 |    8 |    1 |        1
       8 |       2 |        3 |    6 |   11 |    1 |        2
       9 |       2 |        4 |   11 |   13 |    1 |        3
      10 |       2 |        5 |   12 |   -1 |    0 |        4
      11 |       3 |        1 |    2 |    4 |    1 |        0
      12 |       3 |        2 |    5 |   10 |    1 |        1
      13 |       3 |        3 |   10 |   12 |    1 |        2
      14 |       3 |        4 |   11 |   13 |    1 |        3
      15 |       3 |        5 |   12 |   -1 |    0 |        4
      16 |       4 |        1 |    2 |    4 |    1 |        0
      17 |       4 |        2 |    5 |   10 |    1 |        1
      18 |       4 |        3 |   10 |   12 |    1 |        2
      19 |       4 |        4 |   11 |   11 |    1 |        3
      20 |       4 |        5 |    6 |    9 |    1 |        4
      21 |       4 |        6 |    9 |   15 |    1 |        5
      22 |       4 |        7 |   12 |   -1 |    0 |        6
    (22 rows)

Example: | For queries marked as `directed` with `cost` column

The examples in this section use the following Network for queries marked as directed and only cost column is used

    SELECT  * FROM pgr_KSP(
         'SELECT id, source, target, cost FROM edge_table',
          2, 3, 2
       );
     seq | path_id | path_seq | node | edge | cost | agg_cost
    -----+---------+----------+------+------+------+----------
    (0 rows)

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

    SELECT   * FROM pgr_KSP(
         'SELECT id, source, target, cost FROM edge_table',
          2, 12, 2, heap_paths:=true
       );
     seq | path_id | path_seq | node | edge | cost | agg_cost
    -----+---------+----------+------+------+------+----------
       1 |       1 |        1 |    2 |    4 |    1 |        0
       2 |       1 |        2 |    5 |    8 |    1 |        1
       3 |       1 |        3 |    6 |    9 |    1 |        2
       4 |       1 |        4 |    9 |   15 |    1 |        3
       5 |       1 |        5 |   12 |   -1 |    0 |        4
       6 |       2 |        1 |    2 |    4 |    1 |        0
       7 |       2 |        2 |    5 |    8 |    1 |        1
       8 |       2 |        3 |    6 |   11 |    1 |        2
       9 |       2 |        4 |   11 |   13 |    1 |        3
      10 |       2 |        5 |   12 |   -1 |    0 |        4
      11 |       3 |        1 |    2 |    4 |    1 |        0
      12 |       3 |        2 |    5 |   10 |    1 |        1
      13 |       3 |        3 |   10 |   12 |    1 |        2
      14 |       3 |        4 |   11 |   13 |    1 |        3
      15 |       3 |        5 |   12 |   -1 |    0 |        4
    (15 rows)

    SELECT  * FROM pgr_KSP(
         'SELECT id, source, target, cost FROM edge_table',
          2, 12, 2, true, true
       );
     seq | path_id | path_seq | node | edge | cost | agg_cost
    -----+---------+----------+------+------+------+----------
       1 |       1 |        1 |    2 |    4 |    1 |        0
       2 |       1 |        2 |    5 |    8 |    1 |        1
       3 |       1 |        3 |    6 |    9 |    1 |        2
       4 |       1 |        4 |    9 |   15 |    1 |        3
       5 |       1 |        5 |   12 |   -1 |    0 |        4
       6 |       2 |        1 |    2 |    4 |    1 |        0
       7 |       2 |        2 |    5 |    8 |    1 |        1
       8 |       2 |        3 |    6 |   11 |    1 |        2
       9 |       2 |        4 |   11 |   13 |    1 |        3
      10 |       2 |        5 |   12 |   -1 |    0 |        4
      11 |       3 |        1 |    2 |    4 |    1 |        0
      12 |       3 |        2 |    5 |   10 |    1 |        1
      13 |       3 |        3 |   10 |   12 |    1 |        2
      14 |       3 |        4 |   11 |   13 |    1 |        3
      15 |       3 |        5 |   12 |   -1 |    0 |        4
    (15 rows)

Example: | For queries marked as `undirected` with `cost` column

The examples in this section use the following Network for queries marked as undirected and only cost column is used

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

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

## See Also

- https://en.wikipedia.org/wiki/K_shortest_path_routing
- Sample Data network.

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