Typical Sequences Revisited - Algorithms for Linear Orderings of Series Parallel Digraphs

05/09/2019

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by   Hans L. Bodlaender, et al.

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In this paper, we show that the Cutwidth, Modified Cutwidth, and Vertex Separation problems can be solved in O(n^2) time for series parallel digraphs on n vertices. To obtain the result, we give a lemma of independent interest on merges of typical sequences, a notion that was introduced in 1991 [Lagergren and Arnborg, Bodlaender and Kloks, both ICALP '91] to obtain constructive linear time parameterized algorithms for treewidth and pathwidth.