Related papers: Finding Small Hitting Sets in Infinite Range Space…
For a finite set $A\subset \mathbb{R}^d$, let $\Delta(A)$ denote the spread of $A$, which is the ratio of the maximum pairwise distance to the minimum pairwise distance. For a positive integer $n$, let $\gamma_d(n)$ denote the largest…
Selection of a group of representatives satisfying certain fairness constraints, is a commonly occurring scenario. Motivated by this, we initiate a systematic algorithmic study of a \emph{fair} version of \textsc{Hitting Set}. In the…
The (constrained) minimization of a ratio of set functions is a problem frequently occurring in clustering and community detection. As these optimization problems are typically NP-hard, one uses convex or spectral relaxations in practice.…
Imprecise measurements of a point set P = (p1, ..., pn) can be modelled by a family of regions F = (R1, ..., Rn), where each imprecise region Ri contains a unique point pi. A retrieval models an accurate measurement by replacing an…
The transversal hypergraph problem is the task of enumerating the minimal hitting sets of a hypergraph. It is a long-standing open question whether this can be done in output-polynomial time. For hypergraphs whose solutions have bounded…
We develop tractable convex relaxations for rank-constrained quadratic optimization problems over $n \times m$ matrices, a setting for which tractable relaxations are typically only available when the objective or constraints admit spectral…
We study the problem of computing the minimum area triangle that circumscribes a given $n$-sided convex polygon touching edge-to-edge. In other words, we compute the minimum area triangle that is the intersection of 3 half-planes out of $n$…
We introduce an approach to find approximate numerical solutions of truncated bootstrap equations for Conformal Field Theories (CFTs) in arbitrary dimensions. The method is based on a stochastic search via a Metropolis algorithm guided by…
We revisit the classic problem of simplex range searching and related problems in computational geometry. We present a collection of new results which improve previous bounds by multiple logarithmic factors that were caused by the use of…
In this paper, we study the problem of escaping from saddle points in smooth nonconvex optimization problems subject to a convex set $\mathcal{C}$. We propose a generic framework that yields convergence to a second-order stationary point of…
Given a set $S$ of $n$ points in the plane, we consider the problem of answering range selection queries on $S$: that is, given an arbitrary $x$-range $Q$ and an integer $k > 0$, return the $k$-th smallest $y$-coordinate from the set of…
In the dynamic minimum set cover problem, a challenge is to minimize the update time while guaranteeing close to the optimal $\min(O(\log n), f)$ approximation factor. (Throughout, $m$, $n$, $f$, and $C$ are parameters denoting the maximum…
We improve the running times of $O(1)$-approximation algorithms for the set cover problem in geometric settings, specifically, covering points by disks in the plane, or covering points by halfspaces in three dimensions. In the unweighted…
We consider the problem of optimizing an approximately convex function over a bounded convex set in $\mathbb{R}^n$ using only function evaluations. The problem is reduced to sampling from an \emph{approximately} log-concave distribution…
In this paper we propose a convex Sum-of-Squares optimization problem for finding outer approximations of forward reachable sets for nonlinear uncertain Ordinary Differential Equations (ODE's) with either (or both) L2 or point-wise bounded…
We develop two penalty based difference of convex (DC) algorithms for solving chance constrained programs. First, leveraging a rank-based DC decomposition of the chance constraint, we propose a proximal penalty based DC algorithm in the…
We introduce a new measure for planar point sets S that captures a combinatorial distance that S is from being a convex set: The reflexivity rho(S) of S is given by the smallest number of reflex vertices in a simple polygonalization of S.…
While spike trains are obviously not band-limited, the theory of super-resolution tells us that perfect recovery of unknown spike locations and weights from low-pass Fourier transform measurements is possible provided that the minimum…
We develop an adaptive-metric framework for norm-minimization-based outer approximation algorithms in bounded convex vector optimization. The key idea is to let the scalarization metric vary across iterations while measuring approximation…
Let $H$ be a fixed undirected graph on $k$ vertices. The $H$-hitting set problem asks for deleting a minimum number of vertices from a given graph $G$ in such a way that the resulting graph has no copies of $H$ as a subgraph. This problem…