Fast Exponential-Time Algorithms to solve NP-complete ... - Lita
Fast Exponential-Time Algorithms to solve NP-complete ... - Lita
Fast Exponential-Time Algorithms to solve NP-complete ... - Lita
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7/52<strong>Fast</strong> <strong>Exponential</strong>-<strong>Time</strong> <strong>Algorithms</strong>Branching<strong>Time</strong> AnalysisAnalysisAnalysing Branch & Reduce algorithms :Correctness and (Worst Case) Running <strong>Time</strong>Analysis of the Running <strong>Time</strong> :To obtain an Upper Bound on the maximum number of nodesof the search tree (for an input of size n) :1 Define a Measure for a problem instance.2 Lower bound the progress made by the algorithm at eachbranching step.3 Compute the collection of recurrences for all branching andreduction rules.4 Solve all those recurrences (<strong>to</strong> obtain a running time of theform O(αi n ) for each).5 Take the worst case over all solutions.See the surveys [Woeginger (2003), Fomin et al. (2005)].
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