Related papers: Computing the Depth of a Flat
In this note, we develop fast and deterministic dimensionality reduction techniques for a family of subspace approximation problems. Let $P\subset \mathbbm{R}^N$ be a given set of $M$ points. The techniques developed herein find an $O(n…
In a ground-breaking paper, Indyk and Woodruff (STOC 05) showed how to compute $F_k$ (for $k>2$) in space complexity $O(\mbox{\em poly-log}(n,m)\cdot n^{1-\frac2k})$, which is optimal up to (large) poly-logarithmic factors in $n$ and $m$,…
Given an integer k, we consider the parallel k-stripping process applied to a hypergraph H: removing all vertices with degree less than k in each iteration until reaching the k-core of H. Take H as H_r(n,m): a random r-uniform hypergraph on…
Recent empirical evaluations of exact algorithms for Feedback Vertex Set have demonstrated the efficiency of a highest-degree branching algorithm with a degree-based pruning heuristic. In this paper, we prove that this empirically fast…
We study the question of how to compute a point in the convex hull of an input set $S$ of $n$ points in ${\mathbb R}^d$ in a differentially private manner. This question, which is trivial non-privately, turns out to be quite deep when…
$k$-Clustering in $\mathbb{R}^d$ (e.g., $k$-median and $k$-means) is a fundamental machine learning problem. While near-linear time approximation algorithms were known in the classical setting for a dataset with cardinality $n$, it remains…
This paper studies the convergence time of dual gradient methods for general (possibly non-differentiable) strongly convex programs. For general convex programs, the convergence time of dual subgradient/gradient methods with simple running…
In this paper modified variants of the sparse Fourier transform algorithms from [14] are presented which improve on the approximation error bounds of the original algorithms. In addition, simple methods for extending the improved sparse…
This paper proposes an efficient and novel method to address range search on multidimensional points in $\theta(t)$ time, where $t$ is the number of points reported in $\Re^k$ space. This is accomplished by introducing a new data structure,…
In this work we study the time complexity for the search of local minima in random graphs whose vertices have i.i.d. cost values. We show that, for Erd\"os-R\'enyi graphs with connection probability given by $\lambda/n^\alpha$ (with…
Integer programs with m constraints are solvable in pseudo-polynomial time in $\Delta$, the largest coefficient in a constraint, when m is a fixed constant. We give a new algorithm with a running time of $O(\sqrt{m}\Delta)^{2m} + O(nm)$,…
We consider the rooted orienteering problem in Euclidean space: Given $n$ points $P$ in $\mathbb R^d$, a root point $s\in P$ and a budget $\mathcal B>0$, find a path that starts from $s$, has total length at most $\mathcal B$, and visits as…
This article describes novel approaches to quickly estimate planar surfaces from RGBD sensor data. The approach manipulates the standard algebraic fitting equations into a form that allows many of the needed regression variables to be…
In this paper, we consider the following $k$-dispersion problem. Given a set $S$ of $n$ points placed in the plane in a convex position, and an integer $k$ ($0<k<n$), the objective is to compute a subset $S'\subset S$ such that $|S'|=k$ and…
Given a distributed network represented by a weighted undirected graph $G=(V,E)$ on $n$ vertices, and a parameter $k$, we devise a distributed algorithm that computes a routing scheme in $(n^{1/2+1/k}+D)\cdot n^{o(1)}$ rounds, where $D$ is…
Clustering is a fundamental problem in unsupervised machine learning with many applications in data analysis. Popular clustering algorithms such as Lloyd's algorithm and $k$-means++ can take $\Omega(ndk)$ time when clustering $n$ points in…
A transversal of a hypergraph is a set of vertices intersecting each hyperedge. We design and analyze new exponential-time algorithms to enumerate all inclusion-minimal transversals of a hypergraph. For each fixed k>2, our algorithms for…
In this paper we provide faster algorithms for solving the geometric median problem: given $n$ points in $\mathbb{R}^{d}$ compute a point that minimizes the sum of Euclidean distances to the points. This is one of the oldest non-trivial…
The scatter halfspace depth (sHD) is an extension of the location halfspace (also called Tukey) depth that is applicable in the nonparametric analysis of scatter. Using sHD, it is possible to define minimax optimal robust scatter estimators…
Confidence intervals are a standard technique for analyzing data. When applied to time series, confidence intervals are computed for each time point separately. Alternatively, we can compute confidence bands, where we are required to find…