A Tight Subexponential-time Algorithm for Two-Page Book Embedding
<|reference_start|>A Tight Subexponential-time Algorithm for Two-Page Book Embedding: 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(\sqrt{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.<|reference_end|>
@article{ganian2024a,
    title={A Tight Subexponential-time Algorithm for Two-Page Book Embedding},
    author={Robert Ganian, Haiko Mueller, Sebastian Ordyniak, Giacomo Paesani,
  Mateusz Rychlicki},
    journal={arXiv preprint arXiv:2404.14087},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.14087},
    primaryClass={cs.DS cs.CG}
}