Related papers: Nearly Optimal Distinct Elements and Heavy Hitters…

For each $p \in (0,2]$, we present a randomized algorithm that returns an $\epsilon$-approximation of the $p$th frequency moment of a data stream $F_p = \sum_{i = 1}^n \abs{f_i}^p$. The algorithm requires space $O(\epsilon^{-2} \log…

The $\ell_p$ subspace approximation problem is an NP-hard low rank approximation problem that generalizes the median hyperplane ($p = 1$), principal component analysis ($p = 2$), and center hyperplane problems ($p = \infty$). A popular…

In this paper we study how to perform distinct sampling in the streaming model where data contain near-duplicates. The goal of distinct sampling is to return a distinct element uniformly at random from the universe of elements, given that…

In multiple-choice data structures each element $x$ in a set $S$ of $m$ keys is associated with a random set $e(x) \subseteq [n]$ of buckets with capacity $\ell \geq 1$ by hash functions. This setting is captured by the hypergraph $H =…

We consider the distinct elements problem, where the goal is to estimate the number of distinct colors in an urn containing $ k $ balls based on $n$ samples drawn with replacements. Based on discrete polynomial approximation and…

We devise a deterministic algorithm to efficiently sample high-quality solutions of certain spin-glass systems that encode hard optimization problems. We employ tensor networks to represent the Gibbs distribution of all possible…

We consider the the problem of tracking heavy hitters and quantiles in the distributed streaming model. The heavy hitters and quantiles are two important statistics for characterizing a data distribution. Let $A$ be a multiset of elements,…

Clustering is an important technique for identifying structural information in large-scale data analysis, where the underlying dataset may be too large to store. In many applications, recent data can provide more accurate information and…

We give improved hitting sets for two special cases of Read-once Oblivious Arithmetic Branching Programs (ROABP). First is the case of an ROABP with known order of the variables. The best previously known hitting set for this case had size…

This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…

In the adversarially robust streaming model, a stream of elements is presented to an algorithm and is allowed to depend on the output of the algorithm at earlier times during the stream. In the classic insertion-only model of data streams,…

We study a geometric hitting-set problem in which the input consists of a set $P$ of weighted points and a family $S=H\cup V$ of axis-parallel segments in the plane. The goal is to select a minimum-weight subset of $P$ that hits every…

Near-integrability is usually associated with smooth small perturbations of smooth integrable systems. Studying integrable mechanical Hamiltonian flows with impacts that respect the symmetries of the integrable structure provides an…

This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a…

We investigate the problem of identity testing for multidimensional histogram distributions. A distribution $p: D \rightarrow \mathbb{R}_+$, where $D \subseteq \mathbb{R}^d$, is called a $k$-histogram if there exists a partition of the…

Building on existing $hp$-adaptive algorithms driven by equilibrated-flux estimators from [ESAIM Math. Model. Numer. Anal. 57 (2023), 329--366] and the references therein, we propose a novel $h$-adaptive algorithm for a fixed polynomial…

We extend the multi-pass streaming model to sliding window problems, and address the problem of computing order statistics on fixed-size sliding windows, in the multi-pass streaming model as well as the closely related communication…

We consider the reliable implementation of an adaptive high-order unfitted finite element method on Cartesian meshes for solving elliptic interface problems with geometrically curved singularities. We extend our previous work on the…

The Basic Counting problem [1] is one of the most fundamental and critical streaming problems of sliding window queries over data streams. Given a stream of 0's and 1's, the purpose of this problem is to estimate the number of 1's in the…

In this paper, we construct two lower order mixed elements for the linear elasticity problem in the Hellinger-Reissner formulation, one for the 2D problem and one for the 3D problem, both on macro-element meshes. The discrete stress spaces…