Related papers: Deterministic Sensitivity Oracles for Diameter, Ec…
We study the problem of designing \emph{sublinear spectral clustering oracles} for well-clusterable graphs. Such an oracle is an algorithm that, given query access to the adjacency list of a graph $G$, first constructs a compact data…
Computing the diameter, and more generally, all eccentricities of an undirected graph is an important problem in algorithmic graph theory and the challenge is to identify graph classes for which their computation can be achieved in…
A long line of research about connectivity in the Massively Parallel Computation model has culminated in the seminal works of Andoni et al. [FOCS'18] and Behnezhad et al. [FOCS'19]. They provide a randomized algorithm for low-space MPC with…
Building upon [1], this study aims to introduce fractal geometry into graph theory, and to establish a potential theoretical foundation for complex networks. Specifically, we employ the method of substitution to create and explore…
We introduce two block coordinate descent algorithms for solving optimization problems with ordinary differential equations (ODEs) as dynamical constraints. The algorithms do not need to implement direct or adjoint sensitivity analysis…
We consider the problem of designing fundamental graph algorithms on the model of Massive Parallel Computation (MPC). The input to the problem is an undirected graph $G$ with $n$ vertices and $m$ edges, and with $D$ being the maximum…
We provide a deterministic $\tilde{O}(\log N)$-space algorithm for estimating random walk probabilities on undirected graphs, and more generally Eulerian directed graphs, to within inverse polynomial additive error…
We develop a rigorous framework for deterministic coreset construction in empirical risk minimization (ERM). Our central contribution is the Adaptive Deterministic Uniform-Weight Trimming (ADUWT) algorithm, which constructs a coreset by…
Deep optics has emerged as a promising approach by co-designing optical elements with deep learning algorithms. However, current research typically overlooks the analysis and optimization of manufacturing and assembly tolerances. This…
Uncertainty estimation is a crucial aspect of deploying dependable deep learning models in safety-critical systems. In this study, we introduce a novel and efficient method for deterministic uncertainty estimation called Discriminant…
We develop a deep learning methodology for the simultaneous discovery of multiple nontrivial continuous symmetries across an entire labelled dataset. The symmetry transformations and the corresponding generators are modeled with fully…
Given an undirected $n$-vertex planar graph $G=(V,E,\omega)$ with non-negative edge weight function $\omega:E\rightarrow \mathbb R$ and given an assigned label to each vertex, a vertex-labeled distance oracle is a data structure which for…
We propose a new approach to compute an interval over-approximation of the finite time reachable set for a large class of nonlinear systems. This approach relies on the notions of sensitivity matrices, which are the partial derivatives…
The diameter, radius and eccentricities are natural graph parameters. While these problems have been studied extensively, there are no known dynamic algorithms for them beyond the ones that follow from trivial recomputation after each…
We develop a framework for algorithms finding the diameter in graphs of bounded distance Vapnik-Chervonenkis dimension, in (parameterized) subquadratic time complexity. The class of bounded distance VC-dimension graphs is wide, including,…
We present the first approximate distance oracle for sparse directed networks with time-dependent arc-travel-times determined by continuous, piecewise linear, positive functions possessing the FIFO property. Our approach precomputes…
We study point-to-point distance estimation in hypergraphs, where the query is parameterized by a positive integer s, which defines the required level of overlap for two hyperedges to be considered adjacent. To answer s-distance queries, we…
This paper presents a distributed algorithm to simultaneously compute the diameter, radius and node eccentricity in all nodes of a synchronous network. Such topological information may be useful as input to configure other algorithms.…
Deep neural networks do not discriminate between spurious and causal patterns, and will only learn the most predictive ones while ignoring the others. This shortcut learning behaviour is detrimental to a network's ability to generalize to…
We discuss the problem of adaptive discrete-time signal denoising in the situation where the signal to be recovered admits a "linear oracle" -- an unknown linear estimate that takes the form of convolution of observations with a…