Parameterized Algorithms for Queue Layouts
Abstract
An $h$queue layout of a graph $G$ consists of a linear order of its vertices and a partition of its edges into $h$ queues, such that no two independent edges of the same queue nest. The minimum $h$ such that $G$ admits an $h$queue layout is the queue number of $G$. We present two fixedparameter tractable algorithms that exploit structural properties of graphs to compute optimal queue layouts. As our first result, we show that deciding whether a graph $G$ has queue number $1$ and computing a corresponding layout is fixedparameter tractable when parameterized by the treedepth of $G$. Our second result then uses a more restrictive parameter, the vertex cover number, to solve the problem for arbitrary $h$.
 Publication:

arXiv eprints
 Pub Date:
 August 2020
 arXiv:
 arXiv:2008.08288
 Bibcode:
 2020arXiv200808288B
 Keywords:

 Computer Science  Computational Geometry;
 Computer Science  Data Structures and Algorithms
 EPrint:
 Appears in the Proceedings of the 28th International Symposium on Graph Drawing and Network Visualization (GD 2020)