org.jgrapht.alg.vertexcover

## Class RecursiveExactVCImpl<V,E>

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

public class RecursiveExactVCImpl<V,E>
extends Object
implements VertexCoverAlgorithm<V>
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 $V = \emptyset$ then return $\emptyset$
Choose an arbitrary node $v \in G$
$G1 := (V − v, \left{ e \in E | v \not \in e \right})$
$G2 := (V − v − N(v), \left{ e \in E | e \cap (N(v) \cup v)= \empty \right})$
if $|v \cup VC(G1)| \leq |N(v) \cup VC(G2)|$ then
return $v \cup VC(G1)$
else
return $N(v) \cup VC(G2)$

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
• ### Constructor Detail

• #### RecursiveExactVCImpl

public RecursiveExactVCImpl(Graph<V,E> graph)
Constructs a new GreedyVCImpl instance
Parameters:
graph - input graph
• #### RecursiveExactVCImpl

public RecursiveExactVCImpl(Graph<V,E> graph,
Map<V,Double> vertexWeightMap)
Constructs a new GreedyVCImpl instance
Parameters:
graph - input graph
vertexWeightMap - mapping of vertex weights