pgr_depthFirstSearch - Proposed

pgr_depthFirstSearch — Returns a depth first search traversal of the graph. The graph can be directed or undirected.

_images/boost-inside.jpeg

Boost Graph Inside

Warning

Proposed functions for next mayor release.

  • They are not officially in the current release.
  • They will likely officially be part of the next mayor release:
    • The functions make use of ANY-INTEGER and ANY-NUMERICAL
    • Name might not change. (But still can)
    • Signature might not change. (But still can)
    • Functionality might not change. (But still can)
    • pgTap tests have being done. But might need more.
    • Documentation might need refinement.

Availability

Description

Depth First Search algorithm is a traversal algorithm which starts from a root vertex, goes as deep as possible, and backtracks once a vertex is reached with no adjacent vertices or with all visited adjacent vertices. The traversal continues until all the vertices reachable from the root vertex are visited.

The main Characteristics are:

  • The implementation works for both directed and undirected graphs.
  • Provides the Depth First Search traversal order from a root vertex or from a set of root vertices.
  • An optional non-negative maximum depth parameter to limit the results up to a particular depth.
  • For optimization purposes, any duplicated values in the Root vids are ignored.
  • It does not produce the shortest path from a root vertex to a target vertex.
  • The aggregate cost of traversal is not guaranteed to be minimal.
  • The returned values are ordered in ascending order of start_vid.
  • Depth First Search Running time: \(O(E + V)\)

Signatures

Summary

pgr_depthFirstSearch(Edges SQL, Root vid [, directed] [, max_depth])
pgr_depthFirstSearch(Edges SQL, Root vids [, directed] [, max_depth])

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

Using defaults

Example:From root vertex \(2\) on a directed graph
SELECT * FROM pgr_depthFirstSearch(
    '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 |    5 |    4 |    1 |        1
   4 |     2 |         2 |    8 |    7 |    1 |        2
   5 |     3 |         2 |    7 |    6 |    1 |        3
   6 |     2 |         2 |    6 |    8 |    1 |        2
   7 |     3 |         2 |    9 |    9 |    1 |        3
   8 |     4 |         2 |   12 |   15 |    1 |        4
   9 |     4 |         2 |    4 |   16 |    1 |        4
  10 |     5 |         2 |    3 |    3 |    1 |        5
  11 |     3 |         2 |   11 |   11 |    1 |        3
  12 |     2 |         2 |   10 |   10 |    1 |        2
  13 |     3 |         2 |   13 |   14 |    1 |        3
(13 rows)

Single vertex

pgr_depthFirstSearch(Edges SQL, Root vid [, directed] [, max_depth])

RETURNS SET OF (seq, depth, start_vid, node, edge, cost, agg_cost)
Example:From root vertex \(2\) on an undirected graph, with \(depth <= 2\)
SELECT * FROM pgr_depthFirstSearch(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table
    ORDER BY id',
    2, directed => false, max_depth => 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 |     1 |         2 |    5 |    4 |    1 |        1
   7 |     2 |         2 |    8 |    7 |    1 |        2
   8 |     2 |         2 |   10 |   10 |    1 |        2
(8 rows)

Multiple vertices

pgr_depthFirstSearch(Edges SQL, Root vids [, directed] [, max_depth])

RETURNS SET OF (seq, depth, start_vid, node, edge, cost, agg_cost)
Example:From root vertices \(\{11, 2\}\) on an undirected graph with \(depth <= 2\)
SELECT * FROM pgr_depthFirstSearch(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table
    ORDER BY id',
    ARRAY[11, 2], directed => false, max_depth => 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 |     1 |         2 |    5 |    4 |    1 |        1
   7 |     2 |         2 |    8 |    7 |    1 |        2
   8 |     2 |         2 |   10 |   10 |    1 |        2
   9 |     0 |        11 |   11 |   -1 |    0 |        0
  10 |     1 |        11 |    6 |   11 |    1 |        1
  11 |     2 |        11 |    3 |    5 |    1 |        2
  12 |     2 |        11 |    5 |    8 |    1 |        2
  13 |     2 |        11 |    9 |    9 |    1 |        2
  14 |     1 |        11 |   10 |   12 |    1 |        1
  15 |     2 |        11 |   13 |   14 |    1 |        2
  16 |     1 |        11 |   12 |   13 |    1 |        1
(16 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.

Root vids ARRAY[ANY-INTEGER]

Array of identifiers of the root vertices.

  • Used on Multiple Vertices.
  • For optimization purposes, any duplicated value is ignored.

Optional Parameters

Parameter Type Default Description
directed BOOLEAN true
  • When true Graph is Directed
  • When false the graph is Undirected.
max_depth BIGINT \(9223372036854775807\)

Upper limit for the depth of traversal

  • When value is Negative then throws error

Inner query

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  
  • When positive: edge (source, target) exist on the graph.
  • When negative: edge (source, target) does not exist on the graph.
reverse_cost ANY-NUMERICAL -1
  • When positive: edge (target, source) exist on the graph.
  • When negative: edge (target, source) does not exist on 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.

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.

Additional Examples

The examples of this section are based on the Sample Data network.

Example: No internal ordering on traversal

In the following query, the inner query of the example: “Using defaults” is modified so that the data is entered into the algorithm is given in the reverse ordering of the id.

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

The resulting traversal is different.

The left image shows the result with ascending order of ids and the right image shows with descending order of ids:

ascending descending