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 and queue layouts as well as in determining bounds on the stacknumber and the queuenumber for a variety of graphs. The first tool is a formulation of a queue layout of a graph as a covering of its adjacent matrix with staircases. This tool is of independent interest also, because it leads to efficient algorithms for problems related to sequences, graph theory, and computational geometry and also forms the basis of an efficient scheme to perform matrix computations in parallel on a data driven network. The second tool is obtained by considering separated and mingled layouts of graphs. These tools are used to obtain results in three areas. The first area is stack and queue layouts of directed acyclic graphs (dags). This area is motivated by problems of scheduling parallel processes. We establish the stacknumber and the queuenumber of various classes of dags; present linear time algorithms to recognize 1-stack days and leveled-planar dags; and show that the problems of recognizing 9-stack dags and 4-queue dags are both NP-complete. The second area is stack and queue layouts of partially ordered sets (posets). We establish upper bounds on the queuenumber of a poset in terms of other measures such as length, width, and jumpnumber and lower bounds on the stacknumber and queuenumber of certain classes of posets. The third area is queue layouts of planar graphs. We conjecture that a family of planar graphs--the stellated triangles--has unbounded queuenumber; using separated and mingled layouts, we demonstrate significant progress towards that result.