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

A linear inference is a valid inequality of Boolean algebra in which each variable occurs at most once on each side. In this work we leverage recently developed graphical representations of linear formulae to build an implementation that is…

A new computationally efficient dependence measure, and an adaptive statistical test of independence, are proposed. The dependence measure is the difference between analytic embeddings of the joint distribution and the product of the…

The individualization-refinement paradigm provides a strong toolbox for testing isomorphism of two graphs and indeed, the currently fastest implementations of isomorphism solvers all follow this approach. While these solvers are fast in…

Recent advances in random linear systems on finite fields have paved the way for the construction of constant-time data structures representing static functions and minimal perfect hash functions using less space with respect to existing…

Given a database and a target attribute of interest, how can we tell whether there exists a functional, or approximately functional dependence of the target on any set of other attributes in the data? How can we reliably, without bias to…

Quantum linear system (QLS) solvers are a fundamental class of quantum algorithms used in many potential quantum computing applications, including machine learning and solving differential equations. The performance of quantum algorithms is…

Simple tabulation dates back to Zobrist in 1970. Keys are viewed as c characters from some alphabet A. We initialize c tables h_0, ..., h_{c-1} mapping characters to random hash values. A key x=(x_0, ..., x_{c-1}) is hashed to h_0[x_0]…

The simplex method for linear programming is known to be highly efficient in practice, and understanding its performance from a theoretical perspective is an active research topic. The framework of smoothed analysis, first introduced by…

There are distributed graph algorithms for finding maximal matchings and maximal independent sets in $O(\Delta + \log^* n)$ communication rounds; here $n$ is the number of nodes and $\Delta$ is the maximum degree. The lower bound by Linial…

We obtain a necessary and sufficient condition for the linear independence of solutions of differential equations for hyperlogarithms. The key fact is that the multiplier (i.e. the factor $M$ in the differential equation $dS=MS$) has only…

We investigate the problem of determining a set S of k indistinguishable integers in the range [1,n]. The algorithm is allowed to query an integer $q\in [1,n]$, and receive a response comparing this integer to an integer randomly chosen…

In this paper, we analyze a derivative-free line search method designed for bound-constrained problems. Our analysis demonstrates that this method exhibits a worst-case complexity comparable to other derivative-free methods for…

A loss function measures the discrepancy between the true values (observations) and their estimated fits, for a given instance of data. A loss function is said to be proper (unbiased, Fisher consistent) if the fits are defined over a unit…

Measuring and testing the dependency between multiple random functions is often an important task in functional data analysis. In the literature, a model-based method relies on a model which is subject to the risk of model misspecification,…

Given an increasing sequence of integers $x_1,\ldots,x_n$ from a universe $\{0,\ldots,u-1\}$, the monotone minimal perfect hash function (MMPHF) for this sequence is a data structure that answers the following rank queries: $rank(x) = i$ if…

A history-independent data structure does not reveal the history of operations applied to it, only its current logical state, even if its internal state is examined. This paper studies history-independent concurrent dictionaries, in…

We prove new upper and lower bounds on the number of iterations the $k$-dimensional Weisfeiler-Leman algorithm ($k$-WL) requires until stabilization. For $k \geq 3$, we show that $k$-WL stabilizes after at most $O(kn^{k-1}\log n)$…

We introduce a code-based challenge for automated, open-ended mathematical discovery based on the $k$-server conjecture, a central open problem in competitive analysis. The task is to discover a potential function satisfying a large…

In this work, we consider the maximization of submodular functions constrained by independence systems. Because of the wide applicability of submodular functions, this problem has been extensively studied in the literature, on specialized…

We investigate adaptive sublinear algorithms for detecting monotone patterns in an array. Given fixed $2 \leq k \in \mathbb{N}$ and $\varepsilon > 0$, consider the problem of finding a length-$k$ increasing subsequence in an array $f \colon…