The.Algorithm.Design.Manual.Springer-Verlag.1998

Independent Set and Vertex Cover
problems that revolve around finding special subsets of vertices, the first with representatives of every
edge, the second with no edges. If S is the vertex cover of G, the remaining vertices S-V must form an
independent set, for if there were an edge with both vertices in S-V, then S could not have been a vertex
cover. This gives us a reduction between the two problems:
VertexCover(G,k)
G' = G
k' = |V| - k
Return the answer to IndependentSet(G',k')
Again, a simple reduction shows that the problems are identical. Notice how this translation occurs
without any knowledge of the answer. We transform the input, not the solution. This reduction shows
that the hardness of vertex cover imples that independent set must also be hard. It is easy to reverse the
roles of the two problems in this reduction, thus proving that both of these problems are equally hard.
Next: Clique and Independent Set Up: Simple Reductions Previous: Hamiltonian Cycles
Algorithms
Mon Jun 2 23:33:50 EDT 1997
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