A Tight Subexponential-Time Algorithm for Two-Page Book Embedding

Authors Robert Ganian , Haiko Müller , Sebastian Ordyniak , Giacomo Paesani , Mateusz Rychlicki



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Robert Ganian
  • Algorithms and Complexity Group, TU Wien, Austria
Haiko Müller
  • School of Computing, University of Leeds, UK
Sebastian Ordyniak
  • School of Computing, University of Leeds, UK
Giacomo Paesani
  • School of Computing, University of Leeds, UK
Mateusz Rychlicki
  • School of Computing, University of Leeds, UK

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Robert Ganian, Haiko Müller, Sebastian Ordyniak, Giacomo Paesani, and Mateusz Rychlicki. A Tight Subexponential-Time Algorithm for Two-Page Book Embedding. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 68:1-68:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ICALP.2024.68

Abstract

A book embedding of a graph is a drawing that maps vertices onto a line and edges to simple pairwise non-crossing curves drawn into "pages", which are half-planes bounded by that line. Two-page book embeddings, i.e., book embeddings into 2 pages, are of special importance as they are both NP-hard to compute and have specific applications. We obtain a 2^𝒪(√n) algorithm for computing a book embedding of an n-vertex graph on two pages - a result which is asymptotically tight under the Exponential Time Hypothesis. As a key tool in our approach, we obtain a single-exponential fixed-parameter algorithm for the same problem when parameterized by the treewidth of the input graph. We conclude by establishing the fixed-parameter tractability of computing minimum-page book embeddings when parameterized by the feedback edge number, settling an open question arising from previous work on the problem.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • book embedding
  • page number
  • subexponential algorithms
  • subhamiltonicity
  • feedback edge number

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