pgr_KSP

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

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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 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)

See Also

• K shortest paths - Category

• Sample Data

• https://en.wikipedia.org/wiki/K_shortest_path_routing

Indices and tables

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