We consider the problem of sorting a permutation using a network of data structures as introduced by Knuth and Tarjan. In general the model as considered previously was restricted to networks that are directed acyclic graphs (DAGs) of stacks and/or queues. In this paper we study the question of which are the smallest general graphs that can sort an arbitrary permutation and what is their efficiency. We show that certain two-node graphs can sort in time Θ(n 2 ) and no simpler graph can sort all permutations. We then show that certain three-node graphs sort in time Ω(n 3/2 ), and that there exist graphs of k nodes which can sort in time Θ(nlog k n), which is optimal. © 2010 Elsevier B.V. All rights reserved.
Biedl, T., Golynski, A., Hamel, A. M., Löpez-Ortiz, A., & Munro, J. I. (2010). Sorting with networks of data structures. Discrete Applied Mathematics, 158(15), 1579–1586. https://doi.org/10.1016/j.dam.2010.06.007