相关论文: Revisiting calculation of moments of number of com…
The analyses of many algorithms and data structures (such as digital search trees) for searching and sorting are based on the representation of the keys involved as bit strings and so count the number of bit comparisons. On the other hand,…
Sorting algorithms have attracted a great deal of attention and study, as they have numerous applications to Mathematics, Computer Science and related fields. In this thesis, we first deal with the mathematical analysis of the Quicksort…
This paper gives a straightforward self-contained proof of the formula for the variance of the number of comparisons used by the Quicksort sorting algorithm when pivots are chosen uniformly at random. The result has been known for some time…
Most previous studies of the sorting algorithm QuickSort have used the number of key comparisons as a measure of the cost of executing the algorithm. Here we suppose that the n independent and identically distributed (i.i.d.) keys are each…
We consider a multi-pivot QuickSort algorithm using $K\in\mathbb{N}$ pivot elements to partition a nonsorted list into $K+1$ sublists in order to proceed recursively on these sublists. For the partitioning stage, various strategies are in…
We present numerical results for the probability of bad cases for Quicksort, i.e. cases of input data for which the sorting cost considerably exceeds that of the average. Dynamic programming was used to compute solutions of the recurrence…
Stochastic Kronecker graphs supply a parsimonious model for large sparse real world graphs. They can specify the distribution of a large random graph using only three or four parameters. Those parameters have however proved difficult to…
We introduce and analyse a new, extremely simple, randomised sorting algorithm: - choose a pair of indices $\{i, j\}$ according to some distribution $q$; - sort the elements in positions $i$ and $j$ of the array in ascending order. Choosing…
We review some existing methods for the computation of first order moments on junction trees using Shafer-Shenoy algorithm. First, we consider the problem of first order moments computation as vertices problem in junction trees. In this…
The complexity of the Quicksort algorithm is usually measured by the number of key comparisons used during its execution. When operating on a list of $n$ data, permuted uniformly at random, the appropriately normalized complexity $Y_n$ is…
When algorithms for sorting and searching are applied to keys that are represented as bit strings, we can quantify the performance of the algorithms not only in terms of the number of key comparisons required by the algorithms but also in…
In this paper, we analyse the dual pivot Quicksort, a variant of the standard Quicksort algorithm, in which two pivots are used for the partitioning of the array. We are solving recurrences of the expected number of key comparisons and…
Parametric search has been widely used in geometric algorithms. Cole's improvement provides a way of saving a logarithmic factor in the running time over what is achievable using the standard method. Unfortunately, this improvement comes at…
Using non-linear difference equations, combined with symbolic computations, we make a detailed study of the running times of numerous variants of the celebrated Quicksort algorithms, where we consider the variants of single-pivot and…
We obtain for the Kempner series (i.e. harmonic series where certain digits are excluded from all denominators, for example the digit 9 in base 10) new representations as geometrically convergent series. The coefficients for these…
We provide a probabilistic analysis of the output of Quicksort when comparisons can err.
We analyse a generalisation of the Quicksort algorithm, where k uniformly at random chosen pivots are used for partitioning an array of n distinct keys. Specifically, the expected cost of this scheme is obtained, under the assumption of…
QuickXsort is a highly efficient in-place sequential sorting scheme that mixes Hoare's Quicksort algorithm with X, where X can be chosen from a wider range of other known sorting algorithms, like Heapsort, Insertionsort and Mergesort. Its…
The method of moments is a classical statistical technique for density estimation that solves a system of moment equations to estimate the parameters of an unknown distribution. A fundamental question critical to understanding…
The Quickselect algorithm (also called FIND) is a fundamental algorithm for selecting ranks or quantiles within a set of data. Gr\"ubel and R\"osler showed that the number of key comparisons required by Quickselect considered as a process…