Related papers: Codes for Erasures over Directed Graphs
We study the problem of centralized exact repair of multiple failures in distributed storage. We describe constructions that achieve a new set of interior points under exact repair. The constructions build upon the layered code construction…
This chapter deals with the topic of designing reliable and efficient codes for the storage and retrieval of large quantities of data over storage devices that are prone to failure. For long, the traditional objective has been one of…
Repair operations in distributed storage systems potentially expose the data to malicious acts of passive eavesdroppers or active adversaries, which can be detrimental to the security of the system. This paper presents erasure codes and…
Despite their exceptional error-correcting properties, Reed-Solomon (RS) codes have been overlooked in distributed storage applications due to the common belief that they have poor repair bandwidth: A naive repair approach would require the…
Chord diagrams on circles and their intersection graphs (also known as circle graphs) have been intensively studied, and have many applications to the study of knots and knot invariants, among others. However, chord diagrams on more general…
This paper addresses fundamental challenges in two-dimensional error correction by constructing optimal codes for \emph{criss-cross deletions}. We consider an $ n \times n $ array $\boldsymbol{X}$ over a $ q $-ary alphabet $\Sigma_q := \{0,…
The problem of unsupervised learning node embeddings in graphs is one of the important directions in modern network science. In this work we propose a novel framework, which is aimed to find embeddings by \textit{discriminating…
We focus on erasure codes for distributed storage. The distributed storage setting imposes locality requirements because of easy repair demands on the decoder. We first establish the characterization of various locality properties in terms…
Cooperative regenerating codes are regenerating codes designed to tradeoff storage for repair bandwidth in case of multiple node failures. Minimum storage cooperative regenerating (MSCR) codes are a class of cooperative regenerating codes…
Message passing neural networks iteratively generate node embeddings by aggregating information from neighboring nodes. With increasing depth, information from more distant nodes is included. However, node embeddings may be unable to…
This paper investigates secure storage codes over graphs, where multiple independent source symbols are encoded and stored at graph nodes subject to edge-wise correctness and security constraints. For each edge, a specified subset of source…
The graph isomorphism, subgraph isomorphism, and graph edit distance problems are combinatorial problems with many applications. Heuristic exact and approximate algorithms for each of these problems have been developed for different kinds…
We consider the class of conditional graph patterns (\emph{CGPs}) that allow user to query data graphs with complex patterns that contain negation and predicates. To overcome the prohibitive cost of subgraph isomorphism, we consider…
Erasure coding has been recognized as a powerful method to mitigate delays due to slow or straggling nodes in distributed systems. This work shows that erasure coding of data objects can flexibly handle skews in the request rates. Coding…
We consider network coding for networks experiencing worst-case bit-flip errors, and argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting…
Error correcting codes are defined and important parameters for a code are explained. Parameters of new codes constructed on algebraic surfaces are studied. In particular, codes resulting from blowing up points in $\proj^2$ are briefly…
The technique of \emph{equality saturation}, which equips graphs with an equivalence relation, has proven effective for program optimisation. We give a categorical semantics to these structures, called \emph{e-graphs}, in terms of Cartesian…
Intersection graphs are well-studied in the area of graph algorithms. Some intersection graph classes are known to have algorithms enumerating all unlabeled graphs by reverse search. Since these algorithms output graphs one by one and the…
We consider linear network error correction (LNEC) coding when errors may occur on edges of a communication network of which the topology is known. In this paper, we first revisit and explore the framework of LNEC coding, and then unify two…
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…