相关论文: On the k-Independence Required by Linear Probing a…

Minimal perfect hash functions provide space-efficient and collision-free hashing on static sets. Existing algorithms and implementations that build such functions have practical limitations on the number of input elements they can process,…

We find a searching method on ordered lists that surprisingly outperforms binary searching with respect to average query complexity while retaining minmax optimality. The method is shown to require $O(\log_2\log_2 n)$ queries on average…

It is shown that for cuckoo hashing with a stash as proposed by Kirsch, Mitzenmacher, and Wieder (2008) families of very simple hash functions can be used, maintaining the favorable performance guarantees: with stash size $s$ the…

Let $r,m$ be positive integers. Let $0\le x <1$ be a rational number. Let $\Phi_s(x,z)$ be the $s$-th Lerch function $\sum_{k=0}^{\infty}\tfrac{z^{k+1}}{(k+x+1)^s}$ with $s=1,2,\ldots ,r$. When $x=0$, this is the polylogarithmic function.…

Let a Boolean function be available as a black-box (oracle) and one likes to devise an algorithm to test whether it has certain property or it is $\epsilon$-far from having that property. The efficiency of the algorithm is judged by the…

Iterated hash functions process strings recursively, one character at a time. At each iteration, they compute a new hash value from the preceding hash value and the next character. We prove that iterated hashing can be pairwise independent,…

We develop a framework for approximation limits of polynomial-size linear programs from lower bounds on the nonnegative ranks of suitably defined matrices. This framework yields unconditional impossibility results that are applicable to any…

We develop a Hilbert--Schmidt independence criterion (HSIC)-based framework for testing serial independence in strictly stationary time series. The proposed auto Hilbert--Schmidt independence criterion (AutoHSIC) measures dependence between…

We consider the \emph{approximate minimum selection} problem in presence of \emph{independent random comparison faults}. This problem asks to select one of the smallest $k$ elements in a linearly-ordered collection of $n$ elements by only…

In 1948 Hoeffding devised a nonparametric test that detects dependence between two continuous random variables X and Y, based on the ranking of n paired samples (Xi,Yi). The computation of this commonly-used test statistic takes O(n log n)…

We perform a rigorous runtime analysis for the Univariate Marginal Distribution Algorithm on the LeadingOnes function, a well-known benchmark function in the theory community of evolutionary computation with a high correlation between…

Many tools exist to detect dependence between random variables, a core question across a wide range of machine learning, statistical, and scientific endeavors. Although several statistical tests guarantee eventual detection of any…

We present simple, self-contained proofs of correctness for algorithms for linearity testing and program checking of linear functions on finite subsets of integers represented as n-bit numbers. In addition we explore a generalization of…

In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…

A tabulation-based hash function maps a key into d derived characters indexing random values in tables that are then combined with bitwise xor operations to give the hash. Thorup and Zhang (2004) presented d-wise independent…

We study testing $\pi$-freeness of functions $f:[n]^d\to\mathbb{R}$, where $f$ is $\pi$-free if there there are no $k$ indices $x_1\prec\cdots\prec x_k\in [n]^d$ such that $f(x_i)<f(x_j)$ and $\pi(i) < \pi(j)$ for all $i,j \in [k]$, where…

We study the running time, in terms of first order oracle queries, of differentially private empirical/population risk minimization of Lipschitz convex losses. We first consider the setting where the loss is non-smooth and the optimizer…

It has been observed that certain loss functions can render deep-learning pipelines robust against flaws in the data. In this paper, we support these empirical findings with statistical theory. We especially show that empirical-risk…

We consider a static data structure problem of computing a linear operator under cell-probe model. Given a linear operator $M \in \mathbb{F}_2^{m \times n}$, the goal is to pre-process a vector $X \in \mathbb{F}_2^n$ into a data structure…

Limit theorems for non-additive probabilities or non-linear expectations are challenging issues which have raised progressive interest recently. The purpose of this paper is to study the strong law of large numbers and the law of the…