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Analysis of Sorting Algorithms by Kolmogorov Complexity  A Survey
, 2003
"... Recently, many results on the computational complexity of sorting algorithms were obtained using Kolmogorov complexity (the incompressibility method). Especially, the usually hard averagecase analysis is ammenable to this method. Here we survey such results about Bubblesort, Heapsort, Shellsort, ..."
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Recently, many results on the computational complexity of sorting algorithms were obtained using Kolmogorov complexity (the incompressibility method). Especially, the usually hard averagecase analysis is ammenable to this method. Here we survey such results about Bubblesort, Heapsort, Shellsort, Dobosiewiczsort, Shakersort, and sorting with stacks and queues in sequential or parallel mode. Especially in the case of Shellsort the uses of Kolmogorov complexity surprisingly easily resolved problems that had stayed open for a long time despite strenuous attacks.
n points independently at random in 2, according to a prescribed n ≤... be the areas of the triangles
"... thus formed, in nondecreasing order. If µ is absolutely continuous with respect to Lebesgue measure, then, under weak conditions, the set {n3∆n i: i ≥ 1} converges as n → ∞ to a Poisson process with a constant intensity κ(µ). This result, and related conclusions, are proved using standard argument ..."
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thus formed, in nondecreasing order. If µ is absolutely continuous with respect to Lebesgue measure, then, under weak conditions, the set {n3∆n i: i ≥ 1} converges as n → ∞ to a Poisson process with a constant intensity κ(µ). This result, and related conclusions, are proved using standard arguments of Poisson approximation, and may be extended to functionals more general than the area of a triangle. It is proved in addition that, if µ is the uniform probability measure on the region S, then κ(µ) ≤ 2/S, where S  denotes the area of S. Equality holds in that κ(µ) = 2/S  if S is convex, and essentially only then. This work generalizes and extends considerably the conclusions of a recent paper of Jiang, Li, and Vitányi. 1. The problem Drop n points independently and uniformly at random into the unit square [0, 1] 2 of R2. Of the ()