Related papers: Tolerant identification with Euclidean balls
We consider identifying codes in binary Hamming spaces F^n, i.e., in binary hypercubes. The concept of identifying codes was introduced by Karpovsky, Chakrabarty and Levitin in 1998. Currently, the subject forms a topic of its own with…
The concept of an identifying code for a graph was introduced by Karpovsky, Chakrabarty, and Levitin in 1998 as the problem of covering the vertices of a graph such that we can uniquely identify any vertex in the graph by examining the…
We call a subset $C$ of vertices of a graph $G$ a $(1,\leq \ell)$-identifying code if for all subsets $X$ of vertices with size at most $\ell$, the sets $\{c\in C |\exists u \in X, d(u,c)\leq 1\}$ are distinct. The concept of identifying…
Locally recoverable codes were introduced by Gopalan et al. in 2012, and in the same year Prakash et al. introduced the concept of codes with locality, which are a type of locally recoverable codes. In this work we introduce a new family of…
A detection system, modeled in a graph, is composed of "detectors" positioned at a subset of vertices in order to uniquely locate an ``intruder" at any vertex. \emph{Identifying codes} use detectors that can sense the presence or absence of…
When we represent a network of sensors in Euclidean space by a graph, there are two distances between any two nodes that we may consider. One of them is the Euclidean distance. The other is the distance between the two nodes in the graph,…
Linear network coding transmits information in terms of a basis of a vector space and the information is received as a basis of a possible altered vectorspace. Ralf Koetter and Frank R. Kschischang in Coding for errors and erasures in…
We introduce a new family of codes, termed weighted superimposed codes (WSCs). This family generalizes the class of Euclidean superimposed codes (ESCs), used in multiuser identification systems. WSCs allow for discriminating all bounded,…
We revisit the problem of finding small $\epsilon$-separation keys introduced by Motwani and Xu (2008). In this problem, the input is $m$-dimensional tuples $x_1,x_2,\ldots,x_n $. The goal is to find a small subset of coordinates that…
Assume that a graph $G$ models a detection system for a facility with a possible ``intruder," or a multiprocessor network with a possible malfunctioning processor. We consider the problem of placing detectors at a subset of vertices in $G$…
We give nearly optimal bounds on the sample complexity of $(\widetilde{\Omega}(\epsilon),\epsilon)$-tolerant testing the $\rho$-independent set property in the dense graph setting. In particular, we give an algorithm that inspects a random…
We initiate a systematic study of tolerant testers of image properties or, equivalently, algorithms that approximate the distance from a given image to the desired property (that is, the smallest fraction of pixels that need to change in…
In this paper, we present a novel error measure to compare a segmentation against ground truth. This measure, which we call Tolerant Edit Distance (TED), is motivated by two observations: (1) Some errors, like small boundary shifts, are…
Identification is a communication paradigm that promises exponential advantages over transmission for applications that do not actually require all messages to be reliably transmitted. Notably, the identification capacity theorems prove…
We study the problems of identity and closeness testing of $n$-dimensional product distributions. Prior works by Canonne, Diakonikolas, Kane and Stewart (COLT 2017) and Daskalakis and Pan (COLT 2017) have established tight sample complexity…
We suggest a robust nearest-neighbor approach to classifying high-dimensional data. The method enhances sensitivity by employing a threshold and truncates to a sequence of zeros and ones in order to reduce the deleterious impact of…
Identifying codes were introduced by Karpovsky et al. as dominating sets $S\subseteq V(G)$ satisfying $N[u]\cap S \neq N[v]\cap S$ for any distinct vertices $u,v$. Later, Junnila et al. introduced the concept of \emph{self-identifying…
We present a general theory to obtain good linear network codes utilizing the osculating nature of algebraic varieties. In particular, we obtain from the osculating spaces of Veronese varieties explicit families of equidimensional vector…
In this work, we give a novel general approach for distribution testing. We describe two techniques: our first technique gives sample-optimal testers, while our second technique gives matching sample lower bounds. As a consequence, we…
This paper introduces a novel algorithm for cardinality, i.e., the number of nodes, estimation in large scale anonymous graphs using statistical inference methods. Applications of this work include estimating the number of sensor devices,…