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The explosion in the volumes of data being stored online has resulted in distributed storage systems transitioning to erasure coding based schemes. Yet, the codes being deployed in practice are fairly short. In this work, we address what we…
The information-theoretic secure exact-repair regenerating codes for distributed storage systems (DSSs) with parameters $(n,k=d,d,\ell)$ are studied in this paper. We consider distributed storage systems with $n$ nodes, in which the…
The rapid development of signal processing on graphs provides a new perspective for processing large-scale data associated with irregular domains. In many practical applications, it is necessary to handle massive data sets through complex…
We consider the use of distributed storage (DS) to reduce the communication cost of content delivery in wireless networks. Content is stored (cached) in a number of mobile devices using an erasure correcting code. Users retrieve content…
A storage code on a graph $G$ is a set of assignments of symbols to the vertices such that every vertex can recover its value by looking at its neighbors. We consider the question of constructing large-size storage codes on triangle-free…
In distributed storage systems that use coding, the issue of minimizing the communication required to rebuild a storage node after a failure arises. We consider the problem of repairing an erased node in a distributed storage system that…
In order to meet the demands of data-hungry applications, data storage devices are required to be increasingly denser. Various sources of error appear with this increase in density. Multi-dimensional (MD) graph-based codes are capable of…
Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take…
The so-called motorcycle graph has been employed in recent years for various purposes in the context of structured and aligned block decomposition of 2D shapes and 2-manifold surfaces. Applications are in the fields of surface…
Distributed data storage systems are essential to deal with the need to store massive volumes of data. In order to make such a system fault-tolerant, some form of redundancy becomes crucial, incurring various overheads - most prominently in…
It is known that for any general access structure, a secret sharing scheme (SSS) can be constructed from an (m,m)-threshold scheme by using the so-called cumulative map or from a (t,m)-threshold SSS by a modified cumulative map. However,…
Many real-world systems, such as social networks, rely on mining efficiently large graphs, with hundreds of millions of vertices and edges. This volume of information requires partitioning the graph across multiple nodes in a distributed…
Today's era is the digitized era. Managing such generated big data is an important factor for data scientists. Day by day, it increases the demand for big data storage systems. Different organizations are involved in providing…
Erasure coding techniques are getting integrated in networked distributed storage systems as a way to provide fault-tolerance at the cost of less storage overhead than traditional replication. Redundancy is maintained over time through…
Subsystem codes protect quantum information by encoding it in a tensor factor of a subspace of the physical state space. Subsystem codes generalize all major quantum error protection schemes, and therefore are especially versatile. This…
Persistence diagrams (PDs), often characterized as sets of death and birth of homology class, have been known for providing a topological representation of a graph structure, which is often useful in machine learning tasks. Prior works rely…
Constructions of directed configuration graphs based on a given bi-degree distribution were introduced in random graph theory some years ago. These constructions lead to graphs where the degrees of two nodes belonging to the same edge are…
We introduce a neighborhood-based data access model for distributed coded storage allocation. Storage nodes are connected in a generic network and data is accessed locally: a user accesses a randomly chosen storage node, which subsequently…
In the area of distributed graph algorithms a number of network's entities with local views solve some computational task by exchanging messages with their neighbors. Quite unfortunately, an inherent property of most existing distributed…
Memory is an important cognitive function for humans. How a brain with such a small power can complete such a complex memory function, the working mechanism behind this is undoubtedly fascinating. Engram theory views memory as the…