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

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8/52Fast Exponential-Time AlgorithmsBranchingA Simple Branching AlgorithmThe Algorithm sis1 int sis(G = (V , E)) {2 if(|V | = 0) return 0 ;3 choose a vertex v of minimum degree in G4 return 1 + max{sis(G − N[y]) : y ∈ N[v]} ;5 }
9/52Fast Exponential-Time AlgorithmsBranchingA Simple Branching AlgorithmAnalysis of the worst case running timeClassical Analysis and Standard Measure(i.e. the measure of the input size is the number of vertices ofthe input graph).Recurrence :T (n) ≤ (d + 1) · T (n − d − 1),where d is the degree of the chosen vertex v.Solution of recurrence : O((d + 1) n/(d+1) ), being maximumfor d = 2,Running time of sis : O(3 n/3 ).
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Fast Exponential-Time Algorithms to solve NP-complete ... - Lita

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