log n-Approximative NLCk-Decomposition in O(n2k+1) Time

NLCk for k = 1, … is a family of algebras on vertex-labeled graphs introduced by Wanke. An NLC-decomposition of a graph is a derivation of this graph from single vertices using the operations in question. The width of such a decomposition is the number of labels used, and the NLC-width of a graph is the minimum width among its NLC-decompositions. Many difficult graph problems can be solved efficiently with dynamic programming if an NLC-decomposition of low width is given for the input graph. This paper shows that an NLC-decomposition of width at most log n times the optimal width k can be found in O(n 2k+1) time. Related concept: clique-width.

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