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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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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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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.

Cite As Get BibTex

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

Author Details

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

Funding

  • Ganian, Robert: Project No. Y1329 of the Austrian Science Fund (FWF), Project No. ICT22-029 of the Vienna Science Foundation (WWTF).
  • Ordyniak, Sebastian: Project EP/V00252X/1, EPSRC.

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