pgr_primDD¶

pgr_primDD — Catchament nodes using Prim’s algorithm.

Boost Graph Inside¶

Availability

Version 3.0.0
- New Official function

Support

Supported versions: current(3.0)

Description¶

Using Prim algorithm, extracts the nodes that have aggregate costs less than or equal to the value Distance within the calculated minimum spanning tree.

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¶

Summary

pgr_prim(Edges SQL, root vid, distance)
pgr_prim(Edges SQL, root vids, distance)

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

Single vertex¶

pgr_primDD(Edges SQL, root vid, distance)

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

Example: The Minimum Spanning Tree starting on vertex \(2\) with \(agg\_cost <= 3.5\)

SELECT * FROM pgr_primDD(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
    2, 3.5
);
 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
(12 rows)

Multiple vertices¶

pgr_primDD(Edges SQL, root vids, distance)

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

Example: The Minimum Spanning Tree starting on vertices \(\{13, 2\}\) with \(agg\_cost <= 3.5\);

SELECT * FROM pgr_primDD(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
    ARRAY[13,2], 3.5
);
 seq | depth | start_vid | node | edge | cost | agg_cost
-----+-------+-----------+------+------+------+----------
|     0 |         2 |    2 |   -1 |    0 |        0
|     1 |         2 |    1 |    1 |    1 |        1
|     1 |         2 |    3 |    2 |    1 |        1
|     2 |         2 |    4 |    3 |    1 |        2
|     2 |         2 |    6 |    5 |    1 |        2
|     3 |         2 |    9 |    9 |    1 |        3
|     3 |         2 |   11 |   11 |    1 |        3
|     1 |         2 |    5 |    4 |    1 |        1
|     2 |         2 |    8 |    7 |    1 |        2
|     3 |         2 |    7 |    6 |    1 |        3
|     2 |         2 |   10 |   10 |    1 |        2
|     3 |         2 |   13 |   14 |    1 |        3
|     0 |        13 |   13 |   -1 |    0 |        0
|     1 |        13 |   10 |   14 |    1 |        1
|     2 |        13 |    5 |   10 |    1 |        2
|     3 |        13 |    2 |    4 |    1 |        3
|     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 \(0\) gets the spanning forest starting in aleatory nodes for each tree.
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.
Distance	`ANY-NUMERIC`	Upper limit for the inclusion of the node in the result. When the value is Negative throws error

Where:

ANY-INTEGER: SMALLINT, INTEGER, BIGINT
ANY-NUMERIC: SMALLINT, INTEGER, BIGINT, REAL, FLOAT, NUMERIC

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.