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Linear Layouts Revisited: Stacks, Queues, and Exact Algorithms

Authors Thomas Depian , Simon D. Fink , Robert Ganian , Vaishali Surianarayanan

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ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • stack layouts
  • queue layouts
  • parameterized algorithms
  • vertex integrity
  • Ramsey theory

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Abstract

In spite of the extensive study of stack and queue layouts, many fundamental questions remain open concerning the complexity-theoretic frontiers for computing stack and queue layouts. A stack (resp. queue) layout places vertices along a line and assigns edges to pages so that no two edges on the same page are crossing (resp. nested). We provide three new algorithms which together substantially expand our understanding of these problems:  
1) A fixed-parameter algorithm for computing minimum-page stack and queue layouts w.r.t. the vertex integrity of an n-vertex graph G. This result is motivated by an open question in the literature and generalizes the previous algorithms parameterizing by the vertex cover number of G. The proof relies on a newly developed Ramsey pruning technique. Vertex integrity intuitively measures the vertex deletion distance to a subgraph with only small connected components.
2) An n^𝒪(q 𝓁) algorithm for computing 𝓁-page stack and queue layouts of page width at most q. This is the first algorithm avoiding a double-exponential dependency on the parameters. The page width of a layout measures the maximum number of edges one needs to cross on any page to reach the outer face. 
3) A 2^𝒪(n) algorithm for computing 1-page queue layouts. This improves upon the previously fastest n^𝒪(n) algorithm and can be seen as a counterpart to the recent subexponential algorithm for computing 2-page stack layouts [ICALP'24], but relies on an entirely different technique.

Cite As Get BibTex

Thomas Depian, Simon D. Fink, Robert Ganian, and Vaishali Surianarayanan. Linear Layouts Revisited: Stacks, Queues, and Exact Algorithms. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ESA.2025.15

Author Details

Thomas Depian
  • Algorithms and Complexity Group, TU Wien, Austria
Simon D. Fink
  • Algorithms and Complexity Group, TU Wien, Austria
Robert Ganian
  • Algorithms and Complexity Group, TU Wien, Austria
Vaishali Surianarayanan
  • University of California at Santa Barbara, CA, USA

Funding

  • Depian, Thomas: Project No. 10.47379/ICT22029 of the Vienna Science Foundation (WWTF).
  • Fink, Simon D.: Project No. 10.47379/ICT22029 of the Vienna Science Foundation (WWTF) and Project No. 10.55776/Y1329 of the Austrian Science Fund (FWF).
  • Ganian, Robert: Project No. 10.47379/ICT22029 of the Vienna Science Foundation (WWTF) and Projects No. 10.55776/Y1329, 10.55776/COE12 of the Austrian Science Fund (FWF).

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