Related papers: Batch Codes for Asynchronous Recovery of Data
We study the matrix completion problem that leverages hierarchical similarity graphs as side information in the context of recommender systems. Under a hierarchical stochastic block model that well respects practically-relevant social…
We study the problem of learning a hidden hypergraph $G=(V,E)$ by making a single batch of queries (non-adaptively). We consider the hyperedge detection model, in which every query must be of the form: ``Does this set $S\subseteq V$ contain…
The aim of this chapter is to give an overview of the recent advances related to sampling and recovery of signals defined over graphs. First, we illustrate the conditions for perfect recovery of bandlimited graph signals from samples…
We present a general framework for constructing error-correcting codes using distributed graph coloring under the LOCAL model. Building on the correspondence between independent sets in the confusion graph and valid codes, we show that the…
We give an analog of the Myhill-Nerode methods from formal language theory for hypergraphs and use it to derive the following results for two NP-hard hypergraph problems: * We provide an algorithm for testing whether a hypergraph has…
In this paper, we propose a family of label recovery problems on weighted Euclidean random graphs. The vertices of a graph are embedded in $\mathbb{R}^d$ according to a Poisson point process, and are assigned to a discrete community label.…
We present novel non-asymptotic or finite blocklength achievability bounds for three side-information problems in network information theory. These include (i) the Wyner-Ahlswede-Korner (WAK) problem of almost-lossless source coding with…
The linear saturation number $sat^{lin}_k(n,\mathcal{F})$ (linear extremal number $ex^{lin}_k(n,\mathcal{F})$) of $\mathcal{F}$ is the minimum (maximum) number of hyperedges of an $n$-vertex linear $k$-uniform hypergraph containing no…
Consider a $d$-uniform random hypergraph on $n$ vertices in which hyperedges are included iid so that the average degree is $n^\delta$. The projection of a hypergraph is a graph on the same $n$ vertices where an edge connects two vertices…
For two correlated graphs which are independently sub-sampled from a common Erd\H{o}s-R\'enyi graph $\mathbf{G}(n, p)$, we wish to recover their \emph{latent} vertex matching from the observation of these two graphs \emph{without labels}.…
Given two input graphs, finding the largest subgraph that occurs in both, i.e., finding the maximum common subgraph, is a fundamental operator for evaluating the similarity between two graphs in graph data analysis. Existing works for…
Connectivity related concepts are of fundamental interest in graph theory. The area has received extensive attention over four decades, but many problems remain unsolved, especially for directed graphs. A directed graph is 2-edge-connected…
The dynamic trees problem is to maintain a forest undergoing edge insertions and deletions while supporting queries for information such as connectivity. There are many existing data structures for this problem, but few of them are capable…
Zero-error coding encompasses a variety of source and channel problems where the probability of error must be exactly zero. This condition is stricter than that of the vanishing error regime, where the error probability goes to zero as the…
This paper develops a new family of locally recoverable codes for distributed storage systems, Sequential Locally Recoverable Codes (SLRCs) constructed to handle multiple erasures in a sequential recovery approach. We propose a new…
In this paper we give fast distributed graph algorithms for detecting and listing small subgraphs, and for computing or approximating the girth. Our algorithms improve upon the state of the art by polynomial factors, and for girth, we…
Graph burning is a process of information spreading through the network by an agent in discrete steps. The problem is to find an optimal sequence of nodes which have to be given information so that the network is covered in least number of…
The problem of private information retrieval with graph-based replicated storage was recently introduced by Raviv, Tamo and Yaakobi. Its capacity remains open in almost all cases. In this work the asymptotic (large number of messages)…
List-decoding and list-recovery are important generalizations of unique decoding that received considerable attention over the years. However, the optimal trade-off among list-decoding (resp. list-recovery) radius, list size, and the code…
We extend coded distributed computing over finite fields to allow the number of workers to be larger than the field size. We give codes that work for fully general matrix multiplication and show that in this case we serendipitously have…