Sorting 13 Elements Requires 34 Comparisons

Authors:
Marcin Peczarski
Affiliations:
-
Venue:
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Year:
2002

Citing 3
Cited 4

Generating Linear Extensions Fast

SIAM Journal on Computing
The art of computer programming, volume 3: (2nd ed.) sorting and searching

The art of computer programming, volume 3: (2nd ed.) sorting and searching
An Algorithm for Subgraph Isomorphism

Journal of the ACM (JACM)

The Ford--Johnson algorithm still unbeaten for less than 47 elements

Information Processing Letters
Human evaluation of machine translation through binary system comparisons

StatMT '07 Proceedings of the Second Workshop on Statistical Machine Translation
Finding an unknown acyclic orientation of a given graph

Combinatorics, Probability and Computing
Optimal selection and sorting via dynamic programming

Journal of Experimental Algorithmics (JEA)

Quantified Score

Hi-index	0.00

Visualization

Abstract

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