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

  • Authors:

  • Gianni Franceschini

  • Affiliations:

  • Dipartimento di Informatica, Universita di Pisa, Largo B, Pontecorvo 3, 56127 Pisa, Italy

  • Venue:
  • Theory of Computing Systems
  • Year:
  • 2007

  • In-place sorting

    SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science

Quantified Score

Hi-index 0.00

Visualization

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.