pgr_stoerWagner - Experimental - pgRouting Manual (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

Inner query

edges_sql :

an SQL query, which should return a set of rows with the following columns:

Where:

ANY-INTEGER :

SMALLINT, INTEGER, BIGINT

ANY-NUMERICAL :

SMALLINT, INTEGER, BIGINT, REAL, FLOAT

Result Columns

Returns set of (seq, edge, cost, mincut)

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

• https://en.wikipedia.org/wiki/Stoer%E2%80%93Wagner_algorithm

• The queries use the Sample Data network.

Indices and tables

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