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DOI: 10.7155/jgaa.00465
Data Structures and their Planar Graph Layouts
Christopher Auer,
Christian Bachmaier,
Franz J. Brandenburg,
Wolfgang Brunner, and
Andreas Gleißner
Vol. 22, no. 2, pp. 207237, 2018. Regular paper.
Abstract In a stack layout, also known as book embedding, the vertices of a graph
are placed on a line and an edge is a data item that is pushed on the
stack at the left vertex and removed at the right vertex. The LIFO
principle of the stack is represented by a rainbow of nesting edges.
We introduce linear cylindric drawings for the representation of the working
principles of fundamental data structures including stack, queue,
doublestack and deque. The resulting graphs are called stack (queue,
doublestack, deque) graphs. We characterize the feasibility of a sequence
of insertions and removals by planarity and use the graph classes to
compare the relative power of these data structures.
In particular, we show that the deque graphs are the linear cylindric
planar graphs and are the subgraphs of the planar graphs with a
Hamiltonian path. In comparison, the doublestack graphs are the graphs
with a linear layout in the plane and are known as the subgraphs of the
planar graphs with a Hamiltonian cycle. Hence, the power of the queue mode
of a deque is expressed both by the differences between Hamiltonian path
and Hamiltonian cycle and by linear layouts on the cylinder and in the
plane. It is also reflected in the dual graph. Linear cylindric drawings
provide an intuitive planar representation of the FIFO principle of a
queue. We show that a queue graph augmented by a Hamiltonian path has a
dual of the same type and that the dual has an Eulerian path. Finally, we study recognition problems.

Submitted: August 2016.
Reviewed: January 2018.
Revised: February 2018.
Accepted: March 2018.
Final: March 2018.
Published: March 2018.
Communicated by
Giuseppe Di Battista
