Abstract
Many algorithms for sorting n numbers {a 1,a 2,…,a n } proceed by using binary comparisons a i : a j to construct successively stronger partial orders P on {a i } until a linear order emerges (e.g., see Knuth [Kn]). A fundamental quantity in deciding the expected efficiency of such algorithms is Pr(a i < a j ∣ P), the probability that the result of a i :a j is a i < a j when all linear orders consistent with P are equally likely. In this talk we discuss various intuitive but nontrivial properties of Pr(a i < a j ∣ P) and related quantities. The only known proofs of some of these results require the use of the so-called FKG inequality [FKG, SW]. We will describe this powerful result and show how it is used in problems like this.
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© 1982 D. Reidel Publishing Company
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Graham, R.L. (1982). Linear Extensions of Partial Orders and the FKG Inequality. In: Rival, I. (eds) Ordered Sets. NATO Advanced Study Institutes Series, vol 83. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7798-3_6
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DOI: https://doi.org/10.1007/978-94-009-7798-3_6
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