Related papers: Lower Bounds for Testing Directed Acyclicity in th…
We show that for each \ell\geq 4 every sufficiently large oriented graph G with \delta^+(G), \delta^-(G) \geq \lfloor |G|/3 \rfloor +1 contains an \ell-cycle. This is best possible for all those \ell\geq 4 which are not divisible by 3.…
Aim of this paper is to prove necessary and sufficient conditions on the geometry of a domain $\Omega \subset \mathbb{R}^n$ in order that the homogeneous Dirichlet problem for the infinity-Laplace equation in $\Omega$ with constant source…
We lower bound the complexity of finding $\epsilon$-stationary points (with gradient norm at most $\epsilon$) using stochastic first-order methods. In a well-studied model where algorithms access smooth, potentially non-convex functions…
Given a digraph $D=(V,A)$ on $n$ vertices and a vertex $v\in V$, the cycle-degree of $v$ is the minimum size of a set $S \subseteq V(D) \setminus \{v\}$ intersecting every directed cycle of $D$ containing $v$. From this definition of…
We provide a simple proof of convergence covering both the Adam and Adagrad adaptive optimization algorithms when applied to smooth (possibly non-convex) objective functions with bounded gradients. We show that in expectation, the squared…
In this paper, we provide tight lower bounds for the oracle complexity of minimizing high-order H\"older smooth and uniformly convex functions. Specifically, for a function whose $p^{th}$-order derivatives are H\"older continuous with…
We obtain better algorithms for computing more balanced orientations and degree splits in LOCAL. Important to our result is a connection to the hypergraph sinkless orientation problem [BMNSU, SODA'25] We design an algorithm of complexity…
We consider asymptotically flat Riemannian manifolds with nonnegative scalar curvature that are conformal to $\R^{n}\setminus \Omega, n\ge 3$, and so that their boundary is a minimal hypersurface. (Here, $\Omega\subset \R^{n}$ is open…
Augmenting mechanistic ordinary differential equation (ODE) models with machine-learnable structures is an novel approach to create highly accurate, low-dimensional models of engineering systems incorporating both expert knowledge and…
In this paper we consider the problem of testing whether a graph has bounded arboricity. The family of graphs with bounded arboricity includes, among others, bounded-degree graphs, all minor-closed graph classes (e.g. planar graphs, graphs…
Significant progress has been made in developing identification and estimation techniques for missing data problems where modeling assumptions can be described via a directed acyclic graph. The validity of results using such techniques rely…
We give a nearly-optimal algorithm for testing uniformity of distributions supported on $\{-1,1\}^n$, which makes $\tilde O (\sqrt{n}/\varepsilon^2)$ queries to a subcube conditional sampling oracle (Bhattacharyya and Chakraborty (2018)).…
We study minimum degree conditions that guarantee that an $n$-vertex graph is rigid in $\mathbb{R}^d$. For small values of $d$, we obtain a tight bound: for $d = O(\sqrt{n})$, every $n$-vertex graph with minimum degree at least $(n+d)/2 -…
We prove a microlocal lower bound on the mass of high energy eigenfunctions of the Laplacian on compact surfaces of negative curvature, and more generally on surfaces with Anosov geodesic flows. This implies controllability for the…
Caccetta-H\"{a}ggkvist conjecture is a longstanding open problem on degree conditions that force an oriented graph to contain a directed cycle of a bounded length. Motivated by this conjecture, Kelly, K\"uhn, and Osthus initiated a study of…
We show that every $r$-uniform hypergraph on $n$ vertices which does not contain a tight cycle has at most $O(n^{r-1} (\log n)^5)$ edges. This is an improvement on the previously best-known bound, of $n^{r-1} e^{O(\sqrt{\log n})}$, due to…
An $n$-vertex $k$-uniform hypergraph $G$ is $(d,\alpha)$-degenerate if $m_1(G)\le{d}$ and there exists a constant $\varepsilon >0$ such that for every subset $U\subseteq{V(G)}$ with size $2\le|U|\le{\varepsilon n}$, we have…
A \emph{three-dimensional grid drawing} of a graph is a placement of the vertices at distinct points with integer coordinates, such that the straight line segments representing the edges do not cross. Our aim is to produce three-dimensional…
A recent model for property testing of probability distributions (Chakraborty et al., ITCS 2013, Canonne et al., SICOMP 2015) enables tremendous savings in the sample complexity of testing algorithms, by allowing them to condition the…
An oriented multigraph is a directed multigraph without directed 2-cycles. Let ${\rm fas}(D)$ denote the minimum size of a feedback arc set in an oriented multigraph $D$. The degree of a vertex is the sum of its out- and in-degrees. In…