Parameterized Algorithms for Queue Layouts

@inproceedings{Bhore2020ParameterizedAF,
  title={Parameterized Algorithms for Queue Layouts},
  author={S. Bhore and Robert Ganian and Fabrizio Montecchiani and M. N{\"o}llenburg},
  booktitle={Graph Drawing},
  year={2020}
}
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… Expand

References

SHOWING 1-10 OF 31 REFERENCES
On the Queue-Number of Graphs with Bounded Tree-Width
TLDR
It is shown that for each $k\geq1$ graphs with tree-width at most $k$ have queue-number at most £2^k-1, which improves upon double exponential upper bounds due to Dujmovic et al. and Giacomo et al and solves a problem of Rengarajan and Veni Madhavan. Expand
Mixed Linear Layouts: Complexity, Heuristics, and Experiments
TLDR
This work shows NP-completeness results on the recognition problem of certain mixed linear layouts and presents a new heuristic for minimizing conflicts that is an improvement over previous heuristics for linear layouts. Expand
Mixed Linear Layouts of Planar Graphs
  • S. Pupyrev
  • Mathematics, Computer Science
  • Graph Drawing
  • 2017
TLDR
This work disproves the conjecture that every planar graph admits a mixed mixed layout in which every edge is assigned to a stack or to a queue that use a common vertex ordering, and provides a planargraph that does not have such a mixed layout. Expand
Layout of Graphs with Bounded Tree-Width
TLDR
It is proved that the queue-number is bounded by the tree-width, thus resolving an open problem due to Ganley and Heath and disproving a conjecture of Pemmaraju. Expand
Graph layouts via layered separators
  • V. Dujmovic
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. B
  • 2015
TLDR
It is proved that every n-vertex planar graph has track number and queue number at most O(log n), which implies that every planar graphs has a 3D crossing-free grid drawing in O(n log n) volume. Expand
Planar graphs of bounded degree have bounded queue number
TLDR
It is proved that planar graphs of bounded degree (which may have unbounded treewidth) have bounded queue number, which means that every planar graph of boundeddegree admits a three-dimensional straight-line grid drawing in linear volume. Expand
Laying out Graphs Using Queues
TLDR
It is proved that the problem of recognizing 1-queue graphs is NP-complete and relationships between the queuenumber of a graph and its bandwidth and separator size are presented. Expand
Exploring the powers of stacks and queues via graph layouts
In this dissertation we employ graph layouts to explore the relative power of stacks and queues. We first present two tools that are useful in the combinatorial and algorithmic analysis of stack andExpand
Stacks, Queues and Tracks: Layouts of Graph Subdivisions
TLDR
The best known upper bound on the number of division vertices per edge in a 3-stack subdivision of an n-vertex graph G is improved from O(log n) to O (log min\sn(G),qn(G) ), which reduces the question of whether queue-number is bounded by stack-number to whether 3- stack graphs have bounded queue number. Expand
Planar Graphs have Bounded Queue-Number
TLDR
It is proved that every proper minor-closed class of graphs has bounded queue-number, and it is shown that every planar graph is a subgraph of the strong product of a path with some graph of bounded treewidth. Expand
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