Related papers: Online Euclidean Spanners
We study deterministic online embeddings of metrics spaces into normed spaces and into trees against an adaptive adversary. Main results include a polynomial lower bound on the (multiplicative) distortion of embedding into Euclidean spaces,…
We study the problem of high-dimensional robust mean estimation in an online setting. Specifically, we consider a scenario where $n$ sensors are measuring some common, ongoing phenomenon. At each time step $t=1,2,\ldots,T$, the $i^{th}$…
We present two algorithms for maintaining the topological order of a directed acyclic graph with n vertices, under an online edge insertion sequence of m edges. Efficient algorithms for online topological ordering have many applications,…
We study graph spanners for point-set in the high-dimensional Euclidean space. On the one hand, we prove that spanners with stretch <\sqrt{2} and subquadratic size are not possible, even if we add Steiner points. On the other hand, if we…
Computing lower and upper bounds on the competitive ratio of online algorithms is a challenging question: For a minimization combinatorial problem, proving a competitive ratio for a given algorithm leads to an upper bound. However computing…
Given an undirected graph $G=(V,E)$ on $n$ vertices, $m$ edges, and an integer $t\ge 1$, a subgraph $(V,E_S)$, $E_S\subseteq E$ is called a $t$-spanner if for any pair of vertices $u,v \in V$, the distance between them in the subgraph is at…
Adversarial online linear optimization (OLO) is essentially about making performance tradeoffs with respect to the unknown difficulty of the adversary. In the setting of one-dimensional fixed-time OLO on a bounded domain, it has been…
Euclidean spanners are important geometric structures, having found numerous applications over the years. Cornerstone results in this area from the late 80s and early 90s state that for any $d$-dimensional $n$-point Euclidean space, there…
The problem of online checkpointing is a classical problem with numerous applications which had been studied in various forms for almost 50 years. In the simplest version of this problem, a user has to maintain $k$ memorized checkpoints…
We study the online stochastic bipartite matching problem, in a form motivated by display ad allocation on the Internet. In the online, but adversarial case, the celebrated result of Karp, Vazirani and Vazirani gives an approximation ratio…
We provide approximation algorithms for two problems, known as NECKLACE SPLITTING and $\epsilon$-CONSENSUS SPLITTING. In the problem $\epsilon$-CONSENSUS SPLITTING, there are $n$ non-atomic probability measures on the interval $[0, 1]$ and…
We describe an algorithm that takes as input n points in the plane and a parameter {\epsilon}, and produces as output an embedded planar graph having the given points as a subset of its vertices in which the graph distances are a (1 +…
The FOCS'19 paper of Le and Solomon, culminating a long line of research on Euclidean spanners, proves that the lightness (normalized weight) of the greedy $(1+\epsilon)$-spanner in $\mathbb{R}^d$ is $\tilde{O}(\epsilon^{-d})$ for any $d =…
In order to develop practical and efficient algorithms while circumventing overly pessimistic computational lower bounds, recent work has been interested in developing oracle-efficient algorithms in a variety of learning settings. Two such…
We propose a data structure in $d$-dimensional hyperbolic space that can be considered a natural counterpart to quadtrees in Euclidean spaces. Based on this data structure we propose a so-called L-order for hyperbolic point sets, which is…
Online decision making aims to learn the optimal decision rule by making personalized decisions and updating the decision rule recursively. It has become easier than before with the help of big data, but new challenges also come along.…
Spanners for low dimensional spaces (e.g. Euclidean space of constant dimension, or doubling metrics) are well understood. This lies in contrast to the situation in high dimensional spaces, where except for the work of Har-Peled, Indyk and…
We consider the online search problem in which a server starting at the origin of a $d$-dimensional Euclidean space has to find an arbitrary hyperplane. The best-possible competitive ratio and the length of the shortest curve from which…
Conventional hyperparameter optimization methods are computationally intensive and hard to generalize to scenarios that require dynamically adapting hyperparameters, such as life-long learning. Here, we propose an online hyperparameter…
In the online hitting set problem, sets arrive over time, and the algorithm has to maintain a subset of elements that hit all the sets seen so far. Alon, Awerbuch, Azar, Buchbinder, and Naor (SICOMP 2009) gave an algorithm with competitive…