Related papers: Data Stream Algorithms for Codeword Testing
Analyzing patterns in data streams generated by network traffic, sensor networks, or satellite feeds is a challenge for systems in which the available storage is limited. In addition, real data is noisy, which makes designing data stream…
Error-correcting codes are one of the most fundamental objects in pseudorandomness, with applications in communication, complexity theory, and beyond. Codes are useful because of their ability to support decoding, which is the task of…
We present algorithms for the Max-Cover and Max-Unique-Cover problems in the data stream model. The input to both problems are $m$ subsets of a universe of size $n$ and a value $k\in [m]$. In Max-Cover, the problem is to find a collection…
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 work, we show new and improved error-correcting properties of folded Reed-Solomon codes and multiplicity codes. Both of these families of codes are based on polynomials over finite fields, and both have been the sources of recent…
Detection of data races is one of the most important tasks for verifying the correctness of OpenMP parallel codes. Two main models of analysis tools have been proposed for detecting data races: dynamic analysis and static analysis. Dynamic…
Algorithms based on multiple decoding attempts of Reed-Solomon (RS) codes have recently attracted new attention. Choosing decoding candidates based on rate-distortion (R-D) theory, as proposed previously by the authors, currently provides…
Large-scale systems with all-flash arrays have become increasingly common in many computing segments. To make such systems resilient, we can adopt erasure coding such as Reed-Solomon (RS) code as an alternative to replication because…
A natural requirement of many distributed structures is fault-tolerance: after some failures, whatever remains from the structure should still be effective for whatever remains from the network. In this paper we examine spanners of general…
Locally testable codes (LTC) are error-correcting codes that have a local tester which can distinguish valid codewords from words that are "far" from all codewords by probing a given word only at a very few (sublinear, typically constant)…
Given a multiset $X=\{x_1,..., x_n\}$ of real numbers, the {\it floating-point set summation} problem asks for $S_n=x_1+...+x_n$. Let $E^*_n$ denote the minimum worst-case error over all possible orderings of evaluating $S_n$. We prove that…
We establish an equivalence between two important random ensembles of linear codes: random linear codes (RLCs) and random Reed-Solomon (RS) codes. Specifically, we show that these models exhibit identical behavior with respect to key…
In a recent breakthrough, Paz and Schwartzman (SODA'17) presented a single-pass ($2+\epsilon$)-approximation algorithm for the maximum weight matching problem in the semi-streaming model. Their algorithm uses $O(n\log^2 n)$ bits of space,…
We study space-pass tradeoffs in graph streaming algorithms for parameter estimation and property testing problems such as estimating the size of maximum matchings and maximum cuts, weight of minimum spanning trees, or testing if a graph is…
We present efficient and practical algorithms for a large, distributed system of processors to achieve reliable computations in a secure manner. Specifically, we address the problem of computing a general function of several private inputs…
Big data streams are possibly one of the most essential underlying notions. However, data streams are often challenging to handle owing to their rapid pace and limited information lifetime. It is difficult to collect and communicate stream…
We provide the first streaming algorithm for computing a provable approximation to the $k$-means of sparse Big data. Here, sparse Big Data is a set of $n$ vectors in $\mathbb{R}^d$, where each vector has $O(1)$ non-zeroes entries, and…
We construct the first asymptotically good relaxed locally correctable codes with polylogarithmic query complexity, bringing the upper bound polynomially close to the lower bound of Gur and Lachish (SICOMP 2021). Our result follows from…
We attempt to better understand randomization in local distributed graph algorithms by exploring how randomness is used and what we can gain from it: - We first ask the question of how much randomness is needed to obtain efficient…
We study the problem of solving linear program in the streaming model. Given a constraint matrix $A\in \mathbb{R}^{m\times n}$ and vectors $b\in \mathbb{R}^m, c\in \mathbb{R}^n$, we develop a space-efficient interior point method that…