Perfect Simulation from the Quicksort Limit Distribution
نویسندگان
چکیده
منابع مشابه
Perfect simulation from the Quicksort limit distribution
The weak limit of the normalized number of comparisons needed by the Quicksort algorithm to sort n randomly permuted items is known to be determined implicitly by a distributional fixed-point equation. We give an algorithm for perfect random variate generation from this distribution.
متن کاملExact L-distance from the Limit for Quicksort
Using a recursive approach, we obtain a simple exact expression for the L-distance from the limit in Régnier’s [5] classical limit theorem for the number of key comparisons required by QuickSort. A previous study by Fill and Janson [1] using a similar approach found that the d2-distance is of order between n −1 logn and n−1/2, and another by Neininger and Ruschendorf [4] found that the Zolotare...
متن کاملApproximating the limiting Quicksort distribution
The limiting distribution of the normalized number of comparisons used by Quicksort to sort an array of n numbers is known to be the unique fixed point with zero mean of a certain distributional transformation S. We study the convergence to the limiting distribution of the sequence of distributions obtained by iterating the transformation S, beginning with a (nearly) arbitrary starting distribu...
متن کاملAsymptotic Distribution for Random Median Quicksort
The first complete running time analysis of a stochastic divide and conquer algorithm was given for Quicksort, a sorting algorithm invented 1961 by Hoare. We analyse here the variant Random Median Quicksort. The analysis includes the expectation, the asymptotic distribution, the moments and exponential moments. The asymptotic distribution is characterized by a stochastic fixed point equation. T...
متن کاملExact L^2-distance from the limit for QuickSort key comparisons (extended abstract)
Using a recursive approach, we obtain a simple exact expression for the L-distance from the limit in Régnier’s [5] classical limit theorem for the number of key comparisons required by QuickSort. A previous study by Fill and Janson [1] using a similar approach found that the d2-distance is of order between n −1 log n and n, and another by Neininger and Ruschendorf [4] found that the Zolotarev ζ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Communications in Probability
سال: 2000
ISSN: 1083-589X
DOI: 10.1214/ecp.v5-1024