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Sorting 13 Elements Requires 34 Comparisons

2002; Springer Science+Business Media; Linguagem: Inglês

10.1007/3-540-45749-6_68

1611-3349

Marcin Peczarski,

Data Management and Algorithms

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.