org.jgrapht.alg.vertexcover

Class RecursiveExactVCImpl<V,E>

• Type Parameters:
V - the graph vertex type
E - the graph edge type
All Implemented Interfaces:
MinimumVertexCoverAlgorithm<V,E>, MinimumWeightedVertexCoverAlgorithm<V,E>

public class RecursiveExactVCImpl<V,E>
extends Object
implements MinimumWeightedVertexCoverAlgorithm<V,E>
Finds a minimum vertex cover in a undirected graph. The implementation relies on a recursive algorithm. At each recursive step, the algorithm picks a unvisited vertex v and distinguishes two cases: either v has to be added to the vertex cover or all of its neighbors. In pseudo code, the algorithm (simplified) looks like this:
 
VC(G):
if V = ∅ then return ∅
Choose an arbitrary node v ∈ G
G1 := (V − {v}, { e ∈ E | v ∈/ e })
G2 := (V − {v} − N(v), { e ∈ E | e ∩ (N(v) ∪ {v})= ∅ })
if |{v} ∪ VC(G1)| ≤ |N(v) ∪ VC(G2)| then
return {v} ∪ VC(G1)
else
return N(v) ∪ VC(G2)


To speed up the implementation, memoization and a bounding procedure are used. The current implementation solves instances with 150-250 vertices efficiently to optimality. TODO JK: determine runtime complexity and add it to class description. TODO JK: run this class through a performance profiler
Author:
Joris Kinable
• Nested Class Summary

Nested Classes
Modifier and Type Class and Description
protected class  RecursiveExactVCImpl.BitSetCover
Helper class which represents a vertex cover as a space efficient BitSet
• Nested classes/interfaces inherited from interface org.jgrapht.alg.interfaces.MinimumVertexCoverAlgorithm

MinimumVertexCoverAlgorithm.VertexCover<V>, MinimumVertexCoverAlgorithm.VertexCoverImpl<V>
• Constructor Summary

Constructors
Constructor and Description
RecursiveExactVCImpl()
• Method Summary

All Methods
Modifier and Type Method and Description
MinimumVertexCoverAlgorithm.VertexCover<V> getVertexCover(Graph<V,E> graph)
Computes a vertex cover; all vertices are considered to have equal weight.
MinimumVertexCoverAlgorithm.VertexCover<V> getVertexCover(Graph<V,E> graph, Map<V,Double> vertexWeightMap)
Computes a vertex cover; the weight of each vertex is provided in the in the vertexWeightMap.
• Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• Constructor Detail

• RecursiveExactVCImpl

public RecursiveExactVCImpl()
• Method Detail

• getVertexCover

public MinimumVertexCoverAlgorithm.VertexCover<V> getVertexCover(Graph<V,E> graph)
Description copied from interface: MinimumWeightedVertexCoverAlgorithm
Computes a vertex cover; all vertices are considered to have equal weight.
Specified by:
getVertexCover in interface MinimumVertexCoverAlgorithm<V,E>
Specified by:
getVertexCover in interface MinimumWeightedVertexCoverAlgorithm<V,E>
Parameters:
graph - the graph
Returns:
a vertex cover
• getVertexCover

public MinimumVertexCoverAlgorithm.VertexCover<V> getVertexCover(Graph<V,E> graph,
Map<V,Double> vertexWeightMap)
Description copied from interface: MinimumWeightedVertexCoverAlgorithm
Computes a vertex cover; the weight of each vertex is provided in the in the vertexWeightMap.
Specified by:
getVertexCover in interface MinimumWeightedVertexCoverAlgorithm<V,E>
Parameters:
graph - the input graph
vertexWeightMap - map containing non-negative weights for each vertex
Returns:
a vertex cover