Related papers: Resolving the Optimal Metric Distortion Conjecture
In most social choice settings, the participating agents express their preferences over the different alternatives in the form of linear orderings. While this clearly simplifies preference elicitation, it inevitably leads to poor…
Given $n$ vectors $x_0, x_1, \ldots, x_{n-1}$ in $\{0,1\}^{m}$, how to find two vectors whose pairwise Hamming distance is minimum? This problem is known as the \emph{Closest Pair Problem}. If these vectors are generated uniformly at random…
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…
Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…
In multi-objective optimization, computing the entire non-dominated set (also known as the Pareto front or the Pareto frontier) is often intractable. However, for any multiplicative factor greater than one, an approximation set can be…
Prediction-correction algorithms are a highly effective class of methods for solving pseudo-convex optimization problems. The descent direction of these algorithms can be viewed as an adjustment to the gradient direction based on the…
We develop and analyze a set of new sequential simulation-optimization algorithms for large-scale multi-dimensional discrete optimization via simulation problems with a convexity structure. The "large-scale" notion refers to that the…
Our aim is to estimate the perspective-effected geometric distortion of a scene from a video feed. In contrast to all previous work we wish to achieve this using from low-level, spatio-temporally local motion features used in commercial…
We present a substantially more efficient variant, both in terms of running time and size of preprocessing advice, of the algorithm by Liu, Lyubashevsky, and Micciancio for solving CVPP (the preprocessing version of the Closest Vector…
We consider the problem of matching a metric space $(X,d_X)$ of size $k$ with a subspace of a metric space $(Y,d_Y)$ of size $n \geq k$, assuming that these two spaces have constant doubling dimension $\delta$. More precisely, given an…
An assembly of $n$ voters needs to decide on $t$ independent binary issues. Each voter has opinions about the issues, given by a $t$-bit vector. Anscombe's paradox shows that a policy following the majority opinion in each issue may not…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
Over the years, various algorithms were developed, attempting to imitate the Human Visual System (HVS), and evaluate the perceptual image quality. However, for certain image distortions, the functionality of the HVS continues to be an…
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…
The mirror descent algorithm is known to be effective in situations where it is beneficial to adapt the mirror map to the underlying geometry of the optimization model. However, the effect of mirror maps on the geometry of distributed…
Metric learning aims to embed one metric space into another to benefit tasks like classification and clustering. Although a greatly distorted metric space has a high degree of freedom to fit training data, it is prone to overfitting and…
Mathematical morphology provides a nonlinear framework for image and spatial data processing and analysis. Although there have been many successful applications of mathematical morphology to vector-valued images, such as color and…
We study randomized algorithms for constrained optimization, in abstract frameworks that include, in strictly increasing generality: convex programming; LP-type problems; violator spaces; and a setting we introduce, consistent spaces. Such…
The problem of computing a bi-Lipschitz embedding of a graphical metric into the line with minimum distortion has received a lot of attention. The best-known approximation algorithm computes an embedding with distortion $O(c^2)$, where $c$…
Low-distortional metric embeddings are a crucial component in the modern algorithmic toolkit. In an online metric embedding, points arrive sequentially and the goal is to embed them into a simple space irrevocably, while minimizing the…