Myhill–Nerode Methods for Hypergraphs

René van Bevern, Rodney G. Downey, Michael R. Fellows, Serge Gaspers, Frances A. Rosamond

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

We give an analog of the Myhill–Nerode theorem from formal language theory for hypergraphs and use it to derive the following results for two NP-hard hypergraph problems. (1) We provide an algorithm for testing whether a hypergraph has cutwidth at most  that runs in linear time for constant In terms of parameterized complexity theory, the problem is fixed-parameter linear parameterized by(2) We show that it is not expressible in monadic second-order logic whether a hypergraph has bounded (fractional, generalized) hypertree width. The proof leads us to conjecture that, in terms of parameterized complexity theory, these problems are W[1]-hard parameterized by the incidence treewidth (the treewidth of the incidence graph). Thus, in the form of the Myhill–Nerode theorem for hypergraphs, we obtain a method to derive linear-time algorithms and to obtain indicators for intractability for hypergraph problems parameterized by incidence treewidth.

Original languageEnglish
Pages (from-to)696-729
Number of pages34
JournalAlgorithmica
Volume73
Issue number4
DOIs
Publication statusPublished - 1 Dec 2015
Externally publishedYes

Keywords

  • Automata theory
  • Cutwidth
  • Fixed-parameter algorithms
  • Hypertree width
  • NP-hard problems

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