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 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.