Theory of Computing Systems

, Volume 40, Issue 4, pp 327–353

Sorting Stably, in Place, with O(n log n) Comparisons and O(n) Moves

Article

DOI: 10.1007/s00224-006-1311-1

Cite this article as:
Franceschini, G. Theory Comput Syst (2007) 40: 327. doi:10.1007/s00224-006-1311-1

Abstract

We settle a long-standing open question, namely whether it is possible to sort a sequence of n elements stably (i.e., preserving the original relative order of the equal elements), using O(1) auxiliary space and performing O(n log n) comparisons and O(n) data moves. Munro and Raman stated this problem in J. Algorithms (13, 1992) and gave an in-place but unstable sorting algorithm that performs O(n) data moves and O(n1+ε) comparisons. Subsequently (Algorithmica, 16, 1996) they presented a stable algorithm with these same bounds. Recently, Franceschini and Geffert (FOCS 2003) presented an unstable sorting algorithm that matches the asymptotic lower bounds on all computational resources.

Copyright information

© Springer 2007

Authors and Affiliations

  1. 1.Dipartimento di Informatica, Universita di Pisa, Largo B, Pontecorvo 356127 PisaItaly