Sorting with networks of data structures

  • Authors:

  • Therese Biedl;Alexander Golynski;Angèle M. Hamel;Alejandro López-Ortiz;J. Ian Munro

  • Affiliations:

  • Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada, N2L 3G1;Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada, N2L 3G1;Department of Physics and Computer Science, Wilfrid Laurier University, Waterloo, ON, Canada, N2L 3C5;Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada, N2L 3G1;Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada, N2L 3G1

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2010

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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 @Q(n^2) and no simpler graph can sort all permutations. We then show that certain three-node graphs sort in time @W(n^3^/^2), and that there exist graphs of k nodes which can sort in time @Q(nlog"kn), which is optimal.