, Volume 40, Issue 2, pp 133–145 | Cite as

New Results in Minimum-Comparison Sorting

  • Marcin Peczarski


We prove that sorting 13, 14 and 22 elements requires 34, 38 and 71 comparisons, respectively. This solves a long-standing problem posed by Knuth in his famous book The Art of Computer Programming, Volume 3, Sorting and Searching. The results are due to an efficient implementation of an algorithm for counting linear extensions of a given partial order. We also present some useful heuristics which allow us to decrease the running time of the implementation.

Optimal sorting The Ford–Johnson algorithm Counting linear extensions 


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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Institute of Informatics, Warsaw University, ul. Banacha 2, 02-097 WarszawaPoland

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