pgr_primDFS

pgr_primDFS — Prim algorithm for Minimum Spanning Tree with Depth First Search ordering.

Boost Graph Inside

Availability

• Version 3.0.0

  • New Official function

Support

• Supported versions: current(3.0)

Description

Visits and extracts the nodes information in Depth First Search ordering of the Minimum Spanning Tree created using Prims’s algorithm.

The main Characteristics are:

• It’s implementation is only on undirected graph.

• Process is done only on edges with positive costs.

• When the graph is connected

  • The resulting edges make up a tree

• When the graph is not connected,

  • Finds a minimum spanning tree for each connected component.

  • The resulting edges make up a forest.

• Prim’s running time: \(O(E*log V)\)

• Returned tree nodes from a root vertex are on Depth First Search order

• Depth First Search Running time: \(O(E + V)\)

Signatures

pgr_primDFS(Edges SQL, Root vid [, max_depth])
pgr_primDFS(Edges SQL, Root vids [, max_depth])

RETURNS SET OF (seq, depth, start_vid, node, edge, cost, agg_cost)

Single vertex

pgr_primDFS(Edges SQL, Root vid [, max_depth])

RETURNS SET OF (seq, depth, start_vid, node, edge, cost, agg_cost)

Example

The Minimum Spanning Tree having as root vertex \(2\)

SELECT * FROM pgr_primDFS(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
    2
);
 seq | depth | start_vid | node | edge | cost | agg_cost
-----+-------+-----------+------+------+------+----------
   1 |     0 |         2 |    2 |   -1 |    0 |        0
   2 |     1 |         2 |    1 |    1 |    1 |        1
   3 |     1 |         2 |    3 |    2 |    1 |        1
   4 |     2 |         2 |    4 |    3 |    1 |        2
   5 |     2 |         2 |    6 |    5 |    1 |        2
   6 |     3 |         2 |    9 |    9 |    1 |        3
   7 |     3 |         2 |   11 |   11 |    1 |        3
   8 |     4 |         2 |   12 |   13 |    1 |        4
   9 |     1 |         2 |    5 |    4 |    1 |        1
  10 |     2 |         2 |    8 |    7 |    1 |        2
  11 |     3 |         2 |    7 |    6 |    1 |        3
  12 |     2 |         2 |   10 |   10 |    1 |        2
  13 |     3 |         2 |   13 |   14 |    1 |        3
(13 rows)

Multiple vertices

pgr_primDFS(Edges SQL, Root vids [, max_depth])

RETURNS SET OF (seq, depth, start_vid, node, edge, cost, agg_cost)

Example

The Minimum Spanning Tree starting on vertices \(\{13, 2\}\) with \(depth <= 3\)

SELECT * FROM pgr_primDFS(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
    ARRAY[13,2], max_depth := 3
);
 seq | depth | start_vid | node | edge | cost | agg_cost
-----+-------+-----------+------+------+------+----------
   1 |     0 |         2 |    2 |   -1 |    0 |        0
   2 |     1 |         2 |    1 |    1 |    1 |        1
   3 |     1 |         2 |    3 |    2 |    1 |        1
   4 |     2 |         2 |    4 |    3 |    1 |        2
   5 |     2 |         2 |    6 |    5 |    1 |        2
   6 |     3 |         2 |    9 |    9 |    1 |        3
   7 |     3 |         2 |   11 |   11 |    1 |        3
   8 |     1 |         2 |    5 |    4 |    1 |        1
   9 |     2 |         2 |    8 |    7 |    1 |        2
  10 |     3 |         2 |    7 |    6 |    1 |        3
  11 |     2 |         2 |   10 |   10 |    1 |        2
  12 |     3 |         2 |   13 |   14 |    1 |        3
  13 |     0 |        13 |   13 |   -1 |    0 |        0
  14 |     1 |        13 |   10 |   14 |    1 |        1
  15 |     2 |        13 |    5 |   10 |    1 |        2
  16 |     3 |        13 |    2 |    4 |    1 |        3
  17 |     3 |        13 |    8 |    7 |    1 |        3
(17 rows)

Parameters

Parameter	Type	Description
Edges SQL	TEXT	SQL query described in Inner query.
Root vid	BIGINT	Identifier of the root vertex of the tree. Used on Single vertex When value is \(0\) then gets the spanning forest starting in aleatory nodes for each tree in the forest.
Root vids	ARRAY[ANY-INTEGER]	Array of identifiers of the root vertices. Used on Multiple vertices \(0\) values are ignored For optimization purposes, any duplicated value is ignored.

Optional Parameters

Parameter	Type	Default	Description
max_depth	BIGINT	\(9223372036854775807\)	Upper limit for depth of node in the tree When value is Negative then throws error

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, depth, start_vid, node, edge, cost, agg_cost)

Column	Type	Description
seq	BIGINT	Sequential value starting from \(1\).
depth	BIGINT	Depth of the node. \(0\) when node = start_vid.
start_vid	BIGINT	Identifier of the root vertex. In Multiple Vertices results are in ascending order.
node	BIGINT	Identifier of node reached using edge.
edge	BIGINT	Identifier of the edge used to arrive to node. \(-1\) when node = start_vid.
cost	FLOAT	Cost to traverse edge.
agg_cost	FLOAT	Aggregate cost from start_vid to node.

See Also

• Spanning Tree - Category

• Prim - Family of functions

• The queries use the Sample Data network.

• Boost: Prim’s algorithm documentation

• Wikipedia: Prim’s algorithm

Indices and tables

• Index

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