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The Parameterized Complexity Of Extending Stack Layouts

Authors Thomas Depian , Simon D. Fink , Robert Ganian , Martin Nöllenburg

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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
Martin Nöllenburg
  • Algorithms and Complexity Group, TU Wien, Austria

Funding

All authors acknowledge support from the Vienna Science and Technology Fund (WWTF) [10.47379/ICT22029]. Robert Ganian and Thomas Depian furthermore acknowledge support from the Austrian Science Fund (FWF) [10.55776/Y1329].

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Thomas Depian, Simon D. Fink, Robert Ganian, and Martin Nöllenburg. The Parameterized Complexity Of Extending Stack Layouts. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.GD.2024.12

Abstract

An 𝓁-page stack layout (also known as an 𝓁-page book embedding) of a graph is a linear order of the vertex set together with a partition of the edge set into 𝓁 stacks (or pages), such that the endpoints of no two edges on the same stack alternate. We study the problem of extending a given partial 𝓁-page stack layout into a complete one, which can be seen as a natural generalization of the classical NP-hard problem of computing a stack layout of an input graph from scratch. Given the inherent intractability of the problem, we focus on identifying tractable fragments through the refined lens of parameterized complexity analysis. Our results paint a detailed and surprisingly rich complexity-theoretic landscape of the problem which includes the identification of paraNP-hard, W[1]-hard and XP-tractable, as well as fixed-parameter tractable fragments of stack layout extension via a natural sequence of parameterizations.

Subject Classification

ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
  • Mathematics of computing → Graphs and surfaces
Keywords
  • Stack Layout
  • Drawing Extension
  • Parameterized Complexity
  • Book Embedding

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