pgr_stoerWagner - Experimental

pgr_stoerWagner — Returns the weight of the min-cut of graph using stoerWagner algorithm. Function determines a min-cut and the min-cut weight of a connected, undirected graph implemented by Boost.Graph.

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Boost Graph Inside

Warning

Experimental functions

  • They are not officially of the current release.
  • They likely will not be officially be part of the next release:
    • The functions might not make use of ANY-INTEGER and ANY-NUMERICAL
    • Name might change.
    • Signature might change.
    • Functionality might change.
    • pgTap tests might be missing.
    • Might need c/c++ coding.
    • May lack documentation.
    • Documentation if any might need to be rewritten.
    • Documentation examples might need to be automatically generated.
    • Might need a lot of feedback from the comunity.
    • Might depend on a proposed function of pgRouting
    • Might depend on a deprecated function of pgRouting

Availability

  • Version 2.3.0

    • New Experimental function

Support

  • Supported versions: current(3.0)

Description

In graph theory, the Stoer–Wagner algorithm is a recursive algorithm to solve the minimum cut problem in undirected weighted graphs with non-negative weights. The essential idea of this algorithm is to shrink the graph by merging the most intensive vertices, until the graph only contains two combined vertex sets. At each phase, the algorithm finds the minimum s-t cut for two vertices s and t chosen as its will. Then the algorithm shrinks the edge between s and t to search for non s-t cuts. The minimum cut found in all phases will be the minimum weighted cut of the graph.

A cut is a partition of the vertices of a graph into two disjoint subsets. A minimum cut is a cut for which the size or weight of the cut is not larger than the size of any other cut. For an unweighted graph, the minimum cut would simply be the cut with the least edges. For a weighted graph, the sum of all edges’ weight on the cut determines whether it is a minimum cut.

The main characteristics are:

  • Process is done only on edges with positive costs.
  • It’s implementation is only on undirected graph.
  • Sum of the weights of all edges between the two sets is mincut.
    • A mincut is a cut having the least weight.
  • Values are returned when graph is connected.
    • When there is no edge in graph then EMPTY SET is return.
    • When the graph is unconnected then EMPTY SET is return.
  • Sometimes a graph has multiple min-cuts, but all have the same weight. The this function determines exactly one of the min-cuts as well as its weight.
  • Running time: \(O(V*E + V^2*log V)\).

Signatures

pgr_stoerWagner(edges_sql)

RETURNS SET OF (seq, edge, cost, mincut)
OR EMPTY SET
Example:
  • TBD
pgr_stoerWagner(TEXT edges_sql);
RETURNS SET OF (seq, edge, cost, mincut)
OR EMPTY SET
SELECT * FROM pgr_stoerWagner(
    'SELECT id, source, target, cost, reverse_cost 
        FROM edge_table 
     WHERE id < 17'
);
 seq | edge | cost | mincut 
-----+------+------+--------
   1 |    1 |    1 |      1
(1 row)

Parameters

Parameter Type Default Description
edges_sql TEXT   SQL query as described above.

Inner query

edges_sql:an SQL query, which should return a set of rows with the following columns:
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, edge, cost, mincut)

Column Type Description
seq INT Sequential value starting from 1.
edge BIGINT Edges which divides the set of vertices into two.
cost FLOAT Cost to traverse of edge.
mincut FLOAT Min-cut weight of a undirected graph.

Additional Example:

SELECT * FROM pgr_stoerWagner(
    'SELECT id, source, target, cost, reverse_cost 
        FROM edge_table 
     WHERE id = 18'
);
 seq | edge | cost | mincut 
-----+------+------+--------
   1 |   18 |    1 |      1
(1 row)

Use pgr_connectedComponents( ) function in query:

SELECT * FROM pgr_stoerWagner(
$$
 SELECT id, source, target, cost, reverse_cost FROM edge_table 
    where source = any (ARRAY(SELECT node FROM pgr_connectedComponents(
                            'SELECT id, source, target, cost, reverse_cost FROM edge_table ')
                        WHERE component = 14)
                       ) 
                   OR     
          target = any (ARRAY(SELECT node FROM pgr_connectedComponents(
                            'SELECT id, source, target, cost, reverse_cost FROM edge_table ')
                        WHERE component = 14)
                       )
$$
 );
 seq | edge | cost | mincut 
-----+------+------+--------
   1 |   17 |    1 |      1
(1 row)

See Also

Indices and tables