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- James Allen Fill
- STOC
- 1997

For a large class of examples arising in statistical ph~ics known as attnxtiue spin @ems (e.g., the Ising model), one seeks to sample from a probability distribution T on an enormously large state space, but elementary sampling is ruled out by the infeaaibility of calculating an appropriate normalizing constant. The same difficulty arises in computer… (More)

- James Allen Fill, Svante Janson
- Random Struct. Algorithms
- 2001

The limiting distribution of the normalized number of comparisons used by Quick-sort 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… (More)

- James Allen Fill, Nevin Kapur
- Theor. Comput. Sci.
- 2004

Additive tree functionals represent the cost of many divide-and-conquer algorithms. We derive the limiting distribution of the additive func-tionals induced by toll functions of the form (a) n α when α > 0 and (b) log n (the so-called shape functional) on uniformly distributed binary search trees, sometimes called Catalan trees. The Gaussian law obtained in… (More)

- James Allen Fill
- Theor. Comput. Sci.
- 1996

- James Allen Fill, Nevin Kapur
- Random Struct. Algorithms
- 2005

We derive asymptotics of moments and identify limiting distributions, under the random permutation model on m-ary search trees, for functionals that satisfy recurrence relations of a simple additive form. Many important functionals including the space requirement, internal path length, and the so-called shape functional fall under this framework. The… (More)

- Patrick Bindjeme, James Allen Fill
- ArXiv
- 2012

Using a recursive approach, we obtain a simple exact expression for the L 2-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 −1/2 , and another by Neininger… (More)

- James Allen Fill
- Random Struct. Algorithms
- 1996

- James Allen Fill, Svante Janson
- ArXiv
- 2000

Using Fourier analysis, we prove that the limiting distribution of the standardized random number of comparisons used by Quicksort to sort an array of n numbers has an everywhere positive and infinitely differentiable density f , and that each derivative f (k) enjoys superpolynomial decay at ±∞. In particular, each f (k) is bounded. Our method is… (More)

- James Allen Fill, Svante Janson
- J. Algorithms
- 2002

The number of comparisons X n used by Quicksort to sort an array of n distinct numbers has mean µ n of order n log n and standard deviation of order n. Using different methods, Régnier and Rösler each showed that the normalized variate Y n := (X n −µ n)/n converges in distribution, say to Y ; the distribution of Y can be characterized as the unique fixed… (More)

We revisit the classical QuickSort and QuickSelect algorithms , under a complexity model that fully takes into account the elementary comparisons between symbols composing the records to be processed. Our probabilistic models belong to a broad category of information sources that encompasses memoryless (i.e., independent-symbols) and Markov sources, as well… (More)