相关论文: Algorithms and Lower Bounds for de Morgan Formulas…

This article provides novel analytical results for the Rice function, the incomplete Toronto function and the incomplete Lipschitz-Hankel Integrals. Firstly, upper and lower bounds are derived for the Rice function, $Ie(k,x)$. Secondly,…

In this paper, we study the lower complexity bounds for finite-sum optimization problems, where the objective is the average of $n$ individual component functions. We consider Proximal Incremental First-order (PIFO) algorithms which have…

In this note, we consider the minimum number of NOT operators in a Boolean formula representing a Boolean function. In circuit complexity theory, the minimum number of NOT gates in a Boolean circuit computing a Boolean function $f$ is…

We define nondeterministic communication complexity in the model of communication complexity with help of Babai, Hayes and Kimmel. We use it to prove logarithmic lower bounds on the NOF communication complexity of explicit graph functions,…

Proving that there are problems in $\mathsf{P}^\mathsf{NP}$ that require boolean circuits of super-linear size is a major frontier in complexity theory. While such lower bounds are known for larger complexity classes, existing results only…

Graph Neural Networks (GNNs) have become the standard approach for learning and reasoning over relational data, leveraging the message-passing mechanism that iteratively propagates node embeddings through graph structures. While GNNs have…

Communication lower bounds have long been established for matrix multiplication algorithms. However, most methods of asymptotic analysis have either ignored the constant factors or not obtained the tightest possible values. Recent work has…

Let the randomized query complexity of a relation for error probability $\epsilon$ be denoted by $R_\epsilon(\cdot)$. We prove that for any relation $f \subseteq \{0,1\}^n \times \mathcal{R}$ and Boolean function $g:\{0,1\}^m \rightarrow…

We prove a lower bound $\Omega\left(\frac{k+l}{k^2l^2}N^{2-\frac{k+l+2}{kl}}\right)$ on the maximal possible weight of a $(k,l)$-free (that is, free of all-ones $k\times l$ submatrices) Boolean circulant $N \times N$ matrix. The bound is…

This paper tightens the best known analysis of Hein's 1989 algorithm to infer the topology of a weighted tree based on the lengths of paths between its leaves. It shows that the number of length queries required for a degree-$k$ tree of $n$…

We introduce the \emph{graphical reconfigurable circuits (GRC)} model as an abstraction for distributed graph algorithms whose communication scheme is based on local mechanisms that collectively construct long-range reconfigurable channels…

Motivated by the increasing need to understand the algorithmic foundations of distributed large-scale graph computations, we study a number of fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…

In this article, we focus on the communication costs of three symmetric matrix computations: i) multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK) ii) adding the result of the multiplication of a matrix with…

Non-Gaussian Component Analysis (NGCA) is the statistical task of finding a non-Gaussian direction in a high-dimensional dataset. Specifically, given i.i.d.\ samples from a distribution $P^A_{v}$ on $\mathbb{R}^n$ that behaves like a known…

We consider a class of popular distributed non-convex optimization problems, in which agents connected by a network $\mathcal{G}$ collectively optimize a sum of smooth (possibly non-convex) local objective functions. We address the…

It has long been known that any Boolean function that depends on n input variables has both degree and exact quantum query complexity of Omega(log n), and that this bound is achieved for some functions. In this paper we study the case of…

Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model…

The input to the NP-hard Point Line Cover problem (PLC) consists of a set $P$ of $n$ points on the plane and a positive integer $k$, and the question is whether there exists a set of at most $k$ lines which pass through all points in $P$. A…

In the coordinator model of communication with $s$ servers, given an arbitrary non-negative function $f$, we study the problem of approximating the sum $\sum_{i \in [n]}f(x_i)$ up to a $1 \pm \varepsilon$ factor. Here the vector $x \in R^n$…

Graph Neural Networks (GNNs) are limited in their expressive power, struggle with long-range interactions and lack a principled way to model higher-order structures. These problems can be attributed to the strong coupling between the…