Fast Exponential-Time Algorithms to solve NP-complete ... - Lita

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36/52Fast Exponential-Time AlgorithmsBranchingThe Algorithm of Fomin et al.MirroringDefinitionGiven a node v, a mirror of v is a node u ∈ N 2 (v) such thatN(v) \ N(u) is a (possibly empty) clique. We denote by M(v) theset of mirrors of v.When discarding a node v, one can also discard its mirrors as wellwithout modifying the maximum independent set size.Lemma (Mirroring)For any graph G and for any node v of G :α(G) = max{α(G − {v} − M(v)), 1 + α(G − N[v])}.
36/52Fast Exponential-Time AlgorithmsBranchingThe Algorithm of Fomin et al.MirroringDefinitionGiven a node v, a mirror of v is a node u ∈ N 2 (v) such thatN(v) \ N(u) is a (possibly empty) clique. We denote by M(v) theset of mirrors of v.When discarding a node v, one can also discard its mirrors as wellwithout modifying the maximum independent set size.Lemma (Mirroring)For any graph G and for any node v of G :α(G) = max{α(G − {v} − M(v)), 1 + α(G − N[v])}.
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Fast Exponential-Time Algorithms to solve NP-complete ... - Lita

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