Related papers: A statistical view on exchanges in Quickselect

We introduce several modifications of the partitioning schemes used in Hoare's quicksort and quickselect algorithms, including ternary schemes which identify keys less or greater than the pivot. We give estimates for the numbers of swaps…

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 consider a random interval splitting process, in which the splitting rule depends on the empirical distribution of interval lengths. We show that this empirical distribution converges to a limit almost surely as the number of intervals…

In this paper, we consider the problem of column subset selection. We present a novel analysis of the spectral norm reconstruction for a simple randomized algorithm and establish a new bound that depends explicitly on the sampling…

The evolution of dispersal is a classical question in evolutionary biology, and it has been studied in a wide range of mathematical models. A selection-mutation model, in which the population is structured by space and a phenotypic trait,…

This paper finds the bulk local limit of the swap process of uniformly random sorting networks. The limit object is defined through a deterministic procedure, a local version of the Edelman-Greene algorithm, applied to a two dimensional…

In this paper, we present a framework based on a simple data structure and parameterized algorithms for the problems of finding items in an unsorted list of linearly ordered items based on their rank (selection) or value (search). As a…

An exchangeable random matrix is a random matrix with distribution invariant under any permutation of the entries. For such random matrices, we show, as the dimension tends to infinity, that the empirical spectral distribution tends to the…

There is excitement within the algorithms community about a new partitioning method introduced by Yaroslavskiy. This algorithm renders Quicksort slightly faster than the case when it runs under classic partitioning methods. We show that…

We investigate the distribution of the depth of a node containing a specific key or, equivalently, the number of steps needed to retrieve an item stored in a randomly grown binary search tree. Using a representation in terms of mixed and…

Consider a list of $n$ files whose popularities are random. These files are updated according to the move-to-front rule and we consider the induced Markov chain at equilibrium. We give the exact limiting distribution of the search-cost per…

We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…

The problem of quickest detection of a change in distribution is considered under the assumption that the pre-change distribution is known, and the post-change distribution is only known to belong to a family of distributions…

We explicitly compute the limiting transient distribution of the search-cost in the move-to-front Markov chain when the number of objects tends to infinity, for general families of deterministic or random request rates. Our techniques are…

We present a purely numerical approach in Cartesian grid, for efficient computation of Hartree-Fock (HF) exchange contribution in the HF and density functional theory models. This takes inspiration from a recently developed algorithm [Liu…

We consider systems of stochastic fixed-point equations that arise in the asymptotic analysis of random recursive structures and algorithms such as Quicksort, generalized P\'olya urn processes and path lengths of random recursive trees and…

We consider versions of the FIND algorithm where the pivot element used is the median of a subset chosen uniformly at random from the data. For the median selection we assume that subsamples of size asymptotic to $c \cdot n^\alpha$ are…

In a continuous-time setting, Fill (2010) proved, for a large class of probabilistic sources, that the number of symbol comparisons used by QuickSort, when centered by subtracting the mean and scaled by dividing by time, has a limiting…

We propose and analyze an algorithm to approximate distribution functions and densities of perpetuities. Our algorithm refines an earlier approach based on iterating discretized versions of the fixed point equation that defines the…

We consider first passage percolation on sparse random graphs with prescribed degree distributions and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a…