Parameterized Algorithms for Queue Layouts

TL;DR

This paper introduces fixed-parameter tractable algorithms for computing queue layouts of graphs, leveraging structural graph parameters like treedepth and vertex cover number to efficiently determine queue numbers.

Contribution

The paper presents the first fixed-parameter algorithms for queue layout problems based on treedepth and vertex cover parameters.

Findings

Deciding queue number 1 is fixed-parameter tractable with treedepth.

Computing queue layouts for arbitrary h is fixed-parameter tractable with vertex cover.

Algorithms exploit structural properties to efficiently compute optimal 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 fixed-parameter 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 fixed-parameter 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 $h$.