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

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2/52Fast Exponential-Time AlgorithmsDynamic ProgrammingLawler’s Coloring AlgorithmLet G = (V , E). For every X ⊆ V , compute col(G, X ) := χ(G[X ])by increasing cardinality of X .col(G, ∅) = 0col(G, X ) = 1 + min{col(G, X − S) :S maximal independent set of G[X ]}Thus χ(G) = col(G, V ).
13/52Fast Exponential-Time AlgorithmsDynamic ProgrammingAnalysis of Running TimeA graph on i vertices has at most 3 i/3 maximal independent setsand they can be listed in time O ∗ (3 i/3 ).Thus up to a polynomial factor the running time isn∑i=0( ni)3 i/3 = (1 + 3√ 3) nThe running time of Lawler’s coloring algorithm is O(2.4422 n ).
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Fast Exponential-Time Algorithms to solve NP-complete ... - Lita

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