Related papers: Tight Cell Probe Bounds for Succinct Boolean Matri…

We prove essentially optimal fine-grained lower bounds on the gap between a data structure and a partially retroactive version of the same data structure. Precisely, assuming any one of three standard conjectures, we describe a problem that…

Let $T$ be a string of length $n$ over an integer alphabet of size $\sigma$. In the word RAM model, $T$ can be represented in $O(n /\log_\sigma n)$ space. We show that a representation of all covers of $T$ can be computed in the optimal…

We present a unified framework for proving memory lower bounds for multi-pass streaming algorithms that detect planted structures. Planted structures -- such as cliques or bicliques in graphs, and sparse signals in high-dimensional data --…

We give tight cell-probe bounds for the time to compute convolution, multiplication and Hamming distance in a stream. The cell probe model is a particularly strong computational model and subsumes, for example, the popular word RAM model.…

Understanding the singular value spectrum of a matrix $A \in \mathbb{R}^{n \times n}$ is a fundamental task in countless applications. In matrix multiplication time, it is possible to perform a full SVD and directly compute the singular…

Scaling Bayesian optimisation (BO) to high-dimensional search spaces is a active and open research problems particularly when no assumptions are made on function structure. The main reason is that at each iteration, BO requires to find…

A novel matrix approximation problem is considered herein: observations based on a few fully sampled columns and quasi-polynomial structural side information are exploited. The framework is motivated by quantum chemistry problems wherein…

Low-bit quantized neural networks are of great interest in practical applications because they significantly reduce the consumption of both memory and computational resources. Binary neural networks are memory and computationally efficient…

Modern tracking technology has made the collection of large numbers of densely sampled trajectories of moving objects widely available. We consider a fundamental problem encountered when analysing such data: Given $n$ polygonal curves $S$…

In a seminal work, Micciancio & Voulgaris (2013) described a deterministic single-exponential time algorithm for the Closest Vector Problem (CVP) on lattices. It is based on the computation of the Voronoi cell of the given lattice and thus…

This work presents a discovery to advance the wisdom in a particular Succinct Data Structure: Wavelet Tree (Grossi, Gupta, and Vitter 2003). The discovery is first made by showing the feasibility of Reversed Indexes = Values: for integers…

We prove lower bounds of order $n\log n$ for both the problem to multiply polynomials of degree $n$, and to divide polynomials with remainder, in the model of bounded coefficient arithmetic circuits over the complex numbers. These lower…

We develop a new technique for constructing sparse graphs that allow us to prove near-linear lower bounds on the round complexity of computing distances in the CONGEST model. Specifically, we show an $\widetilde{\Omega}(n)$ lower bound for…

We provide new high-accuracy randomized algorithms for solving linear systems and regression problems that are well-conditioned except for $k$ large singular values. For solving such $d \times d$ positive definite system our algorithms…

Min-plus product of two $n\times n$ matrices is a fundamental problem in algorithm research. It is known to be equivalent to APSP, and in general it has no truly subcubic algorithms. In this paper, we focus on the min-plus product on a…

We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…

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…

Reducing communication - either between levels of a memory hierarchy or between processors over a network - is a key component of performance optimization (in both time and energy) for many problems, including dense linear algebra, particle…

With the growing scale of big data, probabilistic structures receive increasing popularity for efficient approximate storage and query processing. For example, Bloom filters (BF) can achieve satisfactory performance for approximate…

In recent years it has become popular to study dynamic problems in a sensitivity setting: Instead of allowing for an arbitrary sequence of updates, the sensitivity model only allows to apply batch updates of small size to the original input…