pgr_stoerWagner  Experimental¶
pgr_stoerWagner
— Returns the weight of the mincut of graph using stoerWagner algorithm.
Function determines a mincut and the mincut weight of a connected, undirected graph implemented by Boost.Graph.
Warning
Possible server crash
These functions might create a server crash
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 ANYINTEGER and ANYNUMERICAL
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
Description¶
In graph theory, the Stoer–Wagner algorithm is a recursive algorithm to solve the minimum cut problem in undirected weighted graphs with nonnegative 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 st 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 st 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 mincuts, but all have the same weight. The this function determines exactly one of the mincuts 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 

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 

Identifier of the edge. 

source 

Identifier of the first end point vertex of the edge. 

target 

Identifier of the second end point vertex of the edge. 

cost 

Weight of the edge (source, target)


reverse_cost 

1 
Weight of the edge (target, source),

Where:
 ANYINTEGER
SMALLINT, INTEGER, BIGINT
 ANYNUMERICAL
SMALLINT, INTEGER, BIGINT, REAL, FLOAT
Result Columns¶
Returns set of (seq, edge, cost, mincut)
Column 
Type 
Description 

seq 

Sequential value starting from 1. 
edge 

Edges which divides the set of vertices into two. 
cost 

Cost to traverse of edge. 
mincut 

Mincut 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¶
https://en.wikipedia.org/wiki/Stoer%E2%80%93Wagner_algorithm
The queries use the Sample Data network.
Indices and tables