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arXiv · 2409.02833

The Parameterized Complexity of Extending Stack Layouts

Thomas Depian·Simon D. Fink·Robert Ganian·Martin Nöllenburg
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Abstract

An $\ell$-page stack layout (also known as an $\ell$-page book embedding) of a graph is a linear order of the vertex set together with a partition of the edge set into $\ell$ 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 $\ell$-page stack layout into a complete one, which is 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.

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Thomas Depian, Simon D. Fink, Robert Ganian, Martin Nöllenburg. 2024-09-04. The Parameterized Complexity of Extending Stack Layouts. https://doi.org/10.7155/jgaa.v29i3.3221

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