pgr_KSP

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

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Boost Graph Inside

Availability

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
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 departure 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.

Additional Examples

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)