Related papers: Reconciling Similar Sets of Data
Suppose that we have two similar files stored on different computers. We need to send the file from the first computer to the second one trying to minimize the number of bits transmitted. This article presents a survey of results known for…
We study the following one-way asymmetric transmission problem, also a variant of model-based compressed sensing: a resource-limited encoder has to report a small set $S$ from a universe of $N$ items to a more powerful decoder (server). The…
We consider a reconciliation problem, where two hosts wish to synchronize their respective sets. Efficient solutions for minimizing the communication cost between the two hosts have been previously proposed in the literature. However, they…
Given a set of sequences, the distance between pairs of them helps us to find their similarity and derive structural relationship amongst them. For genomic sequences such measures make it possible to construct the evolution tree of…
Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The proposed weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some…
The data-compatibility approach to constrained optimization, proposed here, strives to a point that is "close enough" to the solution set and whose target function value is "close enough" to the constrained minimum value. These notions can…
When approximating binary similarity using the hamming distance between short binary hashes, we show that even if the similarity is symmetric, we can have shorter and more accurate hashes by using two distinct code maps. I.e. by…
We study two fundamental problems in communication, Document Exchange (DE) and Error Correcting Code (ECC). In the first problem, two parties hold two strings, and one party tries to learn the other party's string through communication. In…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
With distributed computing and mobile applications becoming ever more prevalent, synchronizing diverging replicas of the same data is a common problem. Reconciliation -- bringing two replicas of the same data structure as close as possible…
We consider the problem of aligning a pair of databases with correlated entries. We introduce a new measure of correlation in a joint distribution that we call cycle mutual information. This measure has operational significance: it…
We address the problem of computing distances between rankings that take into account similarities between candidates. The need for evaluating such distances is governed by applications as diverse as rank aggregation, bioinformatics, social…
The concepts of similarity and distance are crucial in data mining. We consider the problem of defining the distance between two data sets by comparing summary statistics computed from the data sets. The initial definition of our distance…
We study the Closest Pair Problem in Hamming metric, which asks to find the pair with the smallest Hamming distance in a collection of binary vectors. We give a new randomized algorithm for the problem on uniformly random input…
Persistent homology allows us to create topological summaries of complex data. In order to analyse these statistically, we need to choose a topological summary and a relevant metric space in which this topological summary exists. While…
The most common decision criteria for decoding are maximum likelihood decoding and nearest neighbor decoding. It is well-known that maximum likelihood decoding coincides with nearest neighbor decoding with respect to the Hamming metric on…
New lower bounds on the minimum average Hamming distance of binary codes are derived. The bounds are obtained using linear programming approach.
This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as…
In this letter we consider the ensemble of codes formed by the serial concatenation of a Hamming code and two accumulate codes. We show that this ensemble is asymptotically good, in the sense that most codes in the ensemble have minimum…
Finding interesting symmetrical topological structures in high-dimensional systems is an important problem in statistical machine learning. Limited amount of available high-dimensional data and its sensitivity to noise pose computational…