Elsevier

Discrete Applied Mathematics

Volume 158, Issue 15, 6 August 2010, Pages 1579-1586
Discrete Applied Mathematics

Sorting with networks of data structures

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Abstract

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(n2) and no simpler graph can sort all permutations. We then show that certain three-node graphs sort in time Ω(n3/2), and that there exist graphs of k nodes which can sort in time Θ(nlogkn), which is optimal.

Keywords

Sorting networks
Data structures

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