Related papers: Randomization yields simple O(n log star n) algori…

We present a linear programming based algorithm for computing a spanning tree $T$ of a set $P$ of $n$ points in $\Re^d$, such that its crossing number is $O(\min(t \log n, n^{1-1/d}))$, where $t$ the minimum crossing number of any spanning…

In this paper, we present a deterministic variant of Chan's randomized partition tree [Discret. Comput. Geom., 2012]. This result leads to numerous applications. In particular, for $d$-dimensional simplex range counting (for any constant $d…

Various applications of graphs, in particular applications related to finding shortest paths, naturally get inputs with real weights on the edges. However, for algorithmic or visualization reasons, inputs with integer weights would often be…

Adaptive stochastic gradient algorithms in the Euclidean space have attracted much attention lately. Such explorations on Riemannian manifolds, on the other hand, are relatively new, limited, and challenging. This is because of the…

We consider the well-known problem of enumerating all triangles of an undirected graph. Our focus is on determining the input/output (I/O) complexity of this problem. Let $E$ be the number of edges, $M<E$ the size of internal memory, and…

Graph reconstruction can efficiently detect the underlying topology of massive networks such as the Internet. Given a query oracle and a set of nodes, the goal is to obtain the edge set by performing as few queries as possible. An algorithm…

We show how to efficiently solve a clustering problem that arises in a method to evaluate functions of matrices. The problem requires finding the connected components of a graph whose vertices are eigenvalues of a real or complex matrix and…

We show that the pivoting process associated with one line and $n$ points in $r$-dimensional space may need $\Omega(\log^r n)$ steps in expectation as $n \to \infty$. The only cases for which the bound was known previously were for $r \le…

Metric embedding has become a common technique in the design of algorithms. Its applicability is often dependent on how high the embedding's distortion is. For example, embedding finite metric space into trees may require linear distortion…

We consider the problem of counting straight-edge triangulations of a given set $P$ of $n$ points in the plane. Until very recently it was not known whether the exact number of triangulations of $P$ can be computed asymptotically faster…

We propose a mixed integer programming (MIP) model and iterative algorithms based on topological orders to solve optimization problems with acyclic constraints on a directed graph. The proposed MIP model has a significantly lower number of…

We consider the following problem: given an unsorted array of $n$ elements, and a sequence of intervals in the array, compute the median in each of the subarrays defined by the intervals. We describe a simple algorithm which uses O(n) space…

We introduce a novel approach to perform first-order optimization with orthogonal and unitary constraints. This approach is based on a parametrization stemming from Lie group theory through the exponential map. The parametrization…

In this work, we present a fast distributed algorithm for local potential problems: these are graph problems where the task is to find a locally optimal solution where no node can unilaterally improve the utility in its local neighborhood…

We describe a randomized algorithm that, given a set $P$ of points in the plane, computes the best location to insert a new point $p$, such that the Delaunay triangulation of $P\cup\{p\}$ has the largest possible minimum angle. The expected…

We address the problem of optimizing a Brownian motion. We consider a (random) realization $W$ of a Brownian motion with input space in $[0,1]$. Given $W$, our goal is to return an $\epsilon$-approximation of its maximum using the smallest…

In this paper, we present a low-diameter decomposition algorithm in the LOCAL model of distributed computing that succeeds with probability $1 - 1/poly(n)$. Specifically, we show how to compute an $\left(\epsilon, O\left(\frac{\log…

We continue our investigation of the nested loop approach to the O(n) model on random maps, by extending it to the case where loops may visit faces of arbitrary degree. This allows to express the partition function of the O(n) loop model as…

In the Densest k-Subgraph problem, given a graph G and a parameter k, one needs to find a subgraph of G induced on k vertices that contains the largest number of edges. There is a significant gap between the best known upper and lower…

In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…