Abstract
We consider the standard Quicksort algorithm that sorts n distinct keys with all possible n! orderings of keys being equally likely. Equivalently, we analyze the total path length λn in a randomly built binary search tree. Obtaining the limiting distribution of λn is still an outstanding open problem. In this paper, we establish an integral equation for the probability density of the number of comparisons λn. Then, we investigate the large deviations of λn. We shall show that the left tail of the limiting distribution is much “thinner” (i.e., double exponential) than the right tail (which is only exponential). We use formal asymptotic methods of applied mathematics such as the WKB method and matched asymptotics.
The work was supported by NSF Grant DMS-93-00136 and DOE Grant DE-FG02-93ER25168, as well as by NSF Grants NCR-9415491, NCR-9804760.
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© 1998 Springer-Verlag Berlin Heidelberg
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Knessl, C., Szpankowski, W. (1998). Quicksort Again Revisited. In: Luby, M., Rolim, J.D.P., Serna, M. (eds) Randomization and Approximation Techniques in Computer Science. RANDOM 1998. Lecture Notes in Computer Science, vol 1518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49543-6_27
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DOI: https://doi.org/10.1007/3-540-49543-6_27
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