Related papers: HyperSteiner: Computing Heuristic Hyperbolic Stein…
Developing a unified small-signal model for modern, large-scale power systems that remains accurate across a wide range of operating ranges presents a formidable challenge. Traditional methods, spanning mechanistic modeling, modal…
We develop new dynamically orthogonal tensor methods to approximate multivariate functions and the solution of high-dimensional time-dependent nonlinear partial differential equations (PDEs). The key idea relies on a hierarchical…
We consider the problem of efficiently computing the maximum likelihood estimator in Generalized Linear Models (GLMs) when the number of observations is much larger than the number of coefficients ($n \gg p \gg 1$). In this regime,…
Besides training, mathematical optimization is also used in deep learning to model and solve formulations over trained neural networks for purposes such as verification, compression, and optimization with learned constraints. However,…
Hyperbolicity is a graph parameter related to how much a graph resembles a tree with respect to distances. Its computation is challenging as the main approaches consist in scanning all quadruples of the graph or using fast matrix…
Deep learning has achieved impressive performance in many domains, such as computer vision and natural language processing, but its advantage over classical shallow methods on tabular datasets remains questionable. It is especially…
We study the metric Steiner tree problem in the sublinear query model. In this problem, for a set of $n$ points $V$ in a metric space given to us by means of query access to an $n\times n$ matrix $w$, and a set of terminals $T\subseteq V$,…
Given an undirected graph $G = (V, E)$ and a weight function $w:E \to \mathbb{R}$, the \textsc{Minimum Dominating Tree} problem asks to find a minimum weight sub-tree of $G$, $T = (U, F)$, such that every $v \in V \setminus U$ is adjacent…
The Minimum Weight Steiner Tree (MST) is an important combinatorial optimization problem over networks that has applications in a wide range of fields. Here we discuss a general technique to translate the imposed global connectivity…
Geodesic regular tree structures are essential to combat numerical precision issues that arise while working with large-scale computational hyperbolic geometry and have applications in algorithms based on distances in such tessellations. We…
In this paper, we consider Steiner forest and its generalizations, prize-collecting Steiner forest and k-Steiner forest, when the vertices of the input graph are points in the Euclidean plane and the lengths are Euclidean distances. First,…
A recent breakthrough by Ambainis, Balodis, Iraids, Kokainis, Pr\=usis and Vihrovs (SODA'19) showed how to construct faster quantum algorithms for the Traveling Salesman Problem and a few other NP-hard problems by combining in a novel way…
Hyperbolic machine learning is an emerging field aimed at representing data with a hierarchical structure. However, there is a lack of tools for evaluation and analysis of the resulting hyperbolic data representations. To this end, we…
The existence of Steiner triple systems STS(n) of order n containing no nontrivial subsystem is well known for every admissible n. We generalize this result in two ways. First we define the expander property of 3-uniform hypergraphs and…
Reiter's HS-Tree is one of the most popular diagnostic search algorithms due to its desirable properties and general applicability. In sequential diagnosis, where the addressed diagnosis problem is subject to successive change through the…
We propose a novel relay augmentation strategy for extending the lifetime of a certain class of wireless sensor networks. In this class sensors are located at fixed and pre-determined positions and all communication takes place via…
Triangle counting in hypergraph streams, including both hyper-vertex and hyper-edge triangles, is a fundamental problem in hypergraph analytics, with broad applications. However, existing methods face two key limitations: (i) an incomplete…
We show that in the Klein projective ball model of hyperbolic space, the hyperbolic Voronoi diagram is affine and amounts to clip a corresponding power diagram, requiring however algebraic arithmetic. By considering the lesser-known…
When analysing binary data, the ease at which one can interpret results is very important. Many existing methods, however, discover either models that are difficult to read, or return so many results interpretation becomes impossible. Here,…
This paper studies Minimum Spanning Trees under incomplete information for its vertices. We assume that no information is available on the precise placement of vertices so that it is only known that vertices belong to some neighborhoods…