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.
Research of FM partially supported by Dip. Ingegneria Univ. Perugia, RICBA19FM: “Modelli, algoritmi e sistemi per la visualizzazione di grafi e reti”. RG acknowledges support from the Austrian Science Fund (FWF) grant P 31336, SB and MN acknowledge support from FWF grant P 31119.
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Bhore, S., Ganian, R., Montecchiani, F., Nöllenburg, M. (2020). Parameterized Algorithms for Queue Layouts. In: Auber, D., Valtr, P. (eds) Graph Drawing and Network Visualization. GD 2020. Lecture Notes in Computer Science(), vol 12590. Springer, Cham. https://doi.org/10.1007/978-3-030-68766-3_4
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