Parameterized Algorithms for Queue Layouts
An $h$-queue layout of a graph $G$ consists of a linear order of its vertices and a partition of its edges into $h$ sets, called 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 fixe...
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| Published in: | Journal of graph algorithms and applications Vol. 26; no. 3; pp. 335 - 352 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
01.06.2022
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| ISSN: | 1526-1719, 1526-1719 |
| Online Access: | Get full text |
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| Summary: | An $h$-queue layout of a graph $G$ consists of a linear order of its vertices and a partition of its edges into $h$ sets, called 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 $h$. |
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| ISSN: | 1526-1719 1526-1719 |
| DOI: | 10.7155/jgaa.00597 |