Related papers: Interlinked Cycles for Index Coding: Generalizing …
A cycle double cover (CDC) of an undirected graph is a collection of the graph's cycles such that every edge of the graph belongs to exactly two cycles. We describe a constructive method for generating all the cubic graphs that have a 6-CDC…
Spatially-Coupled (SC)-LDPC codes are known to have outstanding error-correction performance and low decoding latency. Whereas previous works on LDPC and SC-LDPC codes mostly take either an asymptotic or a finite-length design approach, in…
The length of an optimal scalar linear index code of a groupcast index coding problem is equal to the minrank of its side information hypergraph. The side-information hypergraph becomes a side-information graph for a special class of…
Chordal decomposition techniques are used to reduce large structured positive semidefinite matrix constraints in semidefinite programs (SDPs). The resulting equivalent problem contains multiple smaller constraints on the nonzero blocks (or…
In addition to their applications in data storage, communications systems, and consumer electronics, LCD codes -- a class of linear codes -- have been employed in cryptography recently. LCD cyclic codes were referred to as reversible cyclic…
A recent trend in data mining has explored (hyper)graph clustering algorithms for data with categorical relationship types. Such algorithms have applications in the analysis of social, co-authorship, and protein interaction networks, to…
p-Cycles offer ring-like switching speed and mesh-like spare capacity efficiency for protecting network against link failures. This makes them extremely efficient and effective protection technique. p-Cycles can also protect all the links…
This paper introduces the notion of involution module, the first generalization of the modular decomposition of 2-structure which has a unique linear-sized decomposition tree. We derive an O(n^2) decomposition algorithm and we take…
Considering a clique as a conservative definition of community structure, we examine how graph partitioning algorithms interact with cliques. Many popular community-finding algorithms partition the entire graph into non-overlapping…
Universal cycles are generalizations of de Bruijn cycles and Gray codes that were introduced originally by Chung, Diaconis, and Graham in 1992. They have been developed by many authors since, for various combinatorial objects such as…
Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…
A cycle C(k1,k2,...,kn) is the oriented cycle formed of n blocks of lengths k1,k2,...,kn-1 and kn respectively. In 2018 Cohen et al. conjectured that for every positive integers k1,k2,...,kn there exists a constant g(k1,k2,...,kn) such that…
This paper presents a novel graphical approach that counts the number of global 8-cycles on the SCRAM three-layer Tanner graph. SCRAM, which stands for Slotted Coded Random Access Multiplexing, is a joint decoder that is meets challenging…
This paper considers a base station that delivers packets to multiple receivers through a sequence of coded transmissions. All receivers overhear the same transmissions. Each receiver may already have some of the packets as side…
Analysis of complex networks, particularly material networks such as the carbon skeleton of hydrocarbons generated in hydrocarbon pyrolysis in carbon-rich systems, is essential for effectively describing, modeling, and predicting their…
Many polynomial invariants are defined on graphs for encoding the combinatorial information and researching them algebraically. In this paper, we introduce the cycle polynomial and the path polynomial of directed graphs for counting cycles…
We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalizes the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and…
Cyclic codes over finite fields are widely implemented in data storage systems, communication systems, and consumer electronics, as they have very efficient encoding and decoding algorithms. They are also important in theory, as they are…
A cyclic base ordering of a connected graph $G$, is a cyclic ordering of $E(G)$ such that every cyclically consecutive $|V(G)|-1$ edges form a spanning tree. In this project, we study cyclic base ordering of various families of graphs,…
Due to their efficient encoding and decoding algorithms cyclic codes, a subclass of linear codes, have applications in consumer electronics, data storage systems, and communication systems. In this paper, Dickson polynomials of the first…