Related papers: A local limit theorem for Quicksort key comparison…
Dual-pivot quicksort refers to variants of classical quicksort where in the partitioning step two pivots are used to split the input into three segments. This can be done in different ways, giving rise to different algorithms. Recently, a…
Much of the copious literature on the subject of sorting has concentrated on minimizing the number of comparisons and/or exchanges/copies. However, a more appropriate yardstick for the performance of sorting algorithms is based on the total…
We prove a central limit theorem applicable to one dimensional stochastic approximation algorithms that converge to a point where the error terms of the algorithm do not vanish. We show how this applies to a certain class of these…
In this paper, we present a local search-based algorithm for individually fair clustering in the presence of outliers. We consider the individual fairness definition proposed in Jung et al., which requires that each of the $n$ points in the…
Central limit theorems for random walks in quenched random environments have attracted plenty of attention in the past years. More recently still, finer local limit theorems -- yielding a Gaussian density multiplied by a highly oscillatory…
Recent work on distributed graph algorithms [e.g. STOC 2022, ITCS 2022, PODC 2020] has drawn attention to the following open question: are round elimination fixed points a universal technique for proving lower bounds? That is, given a…
We prove that \Omega(n log(n)) comparisons are necessary for any quantum algorithm that sorts n numbers with high success probability and uses only comparisons. If no error is allowed, at least 0.110nlog_2(n) - 0.067n + O(1) comparisons…
We propose a new algorithm for k-means clustering in a distributed setting, where the data is distributed across many machines, and a coordinator communicates with these machines to calculate the output clustering. Our algorithm guarantees…
In this paper we examine sorting on the assumption that we do not know in advance which way to sort a sequence of numbers and we set at work simple local comparison and swap operators whose repeating application ends up in sorted sequences.…
The new dual-pivot Quicksort by Vladimir Yaroslavskiy - used in Oracle's Java runtime library since version 7 - features intriguing asymmetries. They make a basic variant of this algorithm use less comparisons than classic single-pivot…
Randomized smoothing is the dominant standard for provable defenses against adversarial examples. Nevertheless, this method has recently been proven to suffer from important information theoretic limitations. In this paper, we argue that…
One of the cornerstones of the distributed complexity theory is the derandomization result by Chang, Kopelowitz, and Pettie [FOCS 2016]: any randomized LOCAL algorithm that solves a locally checkable labeling problem (LCL) can be…
We study sorting algorithms based on randomized round-robin comparisons. Specifically, we study Spin-the-bottle sort, where comparisons are unrestricted, and Annealing sort, where comparisons are restricted to a distance bounded by a…
We present a new technique to efficiently sample and communicate a large number of elements from a distributed sampling space. When used in the context of a recent LOCAL algorithm for $(\operatorname{degree}+1)$-list-coloring (D1LC), this…
Let $f_n$ be a random polynomial of degree $n$ with i.i.d. mean-zero and finite variance random coefficients. It is well known that the roots of $f_n$ cluster uniformly around the unit circle as $n$ grows large. We give a simple 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…
Let $X_H$ be the number of copies of a fixed graph $H$ in $G(n,p)$. In 2016, Gilmer and Kopparty conjectured that a local central limit theorem should hold for $X_H$ as long as $H$ is connected, $p\gg n^{-1/m(H)}$ and $n^2(1-p)\gg 1$, where…
Fast distributed algorithms that output a feasible solution for constraint satisfaction problems, such as maximal independent sets, have been heavily studied. There has been much less research on distributed sampling problems, where one…
In this paper, we study a class of multiscale McKean-Vlasov stochastic systems where the entire system depends on the distribution of the fast component. First of all, by the Poisson equation method we prove that the slow component…
We show that several versions of Floyd and Rivest's algorithm Select [Comm.\ ACM {\bf 18} (1975) 173] for finding the $k$th smallest of $n$ elements require at most $n+\min\{k,n-k\}+o(n)$ comparisons on average, even when equal elements…