相关论文: A Generalisation of Interlinked Cycle Structures a…

Let $G$ be an $n$-vertex connected graph. A cyclic base ordering of $G$ is a cyclic ordering of all edges such that every cyclically consecutive $n-1$ edges induce a spanning tree of $G$. In this project, we study cyclic base ordering of…

To lower the complexity of network codes over packet line networks with arbitrary schedules, chunked codes (CC) and overlapped chunked codes (OCC) were proposed in earlier works. These codes have been previously analyzed for relatively…

In this paper we define critical graphs as minimal graphs that support a given set of rates for the index coding problem, and study them for both the one-shot and asymptotic setups. For the case of equal rates, we find the critical graph…

In this paper, the problem of designing network codes that are both communicationally and computationally efficient over packet line networks with worst-case schedules is considered. In this context, random linear network codes (dense…

Many common graph data mining tasks take the form of identifying dense subgraphs (e.g. clustering, clique-finding, etc). In biological applications, the natural model for these dense substructures is often a complete bipartite graph…

Partial clique covering is one of the most basic coding schemes for index coding problems, generalizing clique and cycle covering on the side information digraph and further reducing the achievable broadcast rate. In this paper, we start…

The graph of overlapping permutations is a directed graph that is an analogue to the De Bruijn graph. It consists of vertices that are permutations of length $n$ and edges that are permutations of length $n+1$ in which an edge $a_1\cdots…

In Index Coding, the goal is to use a broadcast channel as efficiently as possible to communicate information from a source to multiple receivers which can possess some of the information symbols at the source as side-information. In this…

Universal cycles are generalizations of de Bruijn cycles and Gray codes that were introduced originally by Chung, Diaconis, and Graham in 1990. They have been developed by many authors since, for various combinatorial objects such as…

We introduce the graph parameter readability and study it as a function of the number of vertices in a graph. Given a digraph D, an injective overlap labeling assigns a unique string to each vertex such that there is an arc from x to y if…

We introduce the cycle intersection graph of a graph, an adaptation of the cycle graph of a graph, and use the structure of these graphs to prove an upper bound for the decycling number of all even graphs. This bound is shown to be…

A number of applications of Steiner triple systems (e.g. disk erasure codes) exist that require a special ordering of its blocks. Universal cycles, introduced by Chung, Diaconis, and Graham in 1992, and Gray codes are examples of listing…

We suggest an enhancement to structural coding through the use of (a) causally bound codes, (b) basic constructs of graph theory and (c) statistics. As is the norm with structural coding, the codes are collected into categories. The…

The induced odd cycle packing number $iocp(G)$ of a graph $G$ is the maximum integer $k$ such that $G$ contains an induced subgraph consisting of $k$ pairwise vertex-disjoint odd cycles. Motivated by applications to geometric graphs, Bonamy…

An index coding (IC) problem consisting of a server and multiple receivers with different side-information and demand sets can be equivalently represented using a fitting matrix. A scalar linear index code to a given IC problem is a matrix…

Universal Circuits (UCs) offer a promising approach to hardware Intellectual Property (IP) obfuscation, leveraging cryptographic principles to hide both structure and function in a programmable logic fabric. Their adaptability makes them…

A cycle cover of a bridgeless graph $G$ is a collection of simple cycles in $G$ such that each edge $e$ appears on at least one cycle. The common objective in cycle cover computation is to minimize the total lengths of all cycles. Motivated…

This paper deals with embedded index coding problem (EICP), introduced by A. Porter and M. Wootters, which is a decentralized communication problem among users with side information. An alternate definition of the parameter minrank of an…

In this paper, we propose new coupled codes constructed by overlapping circular spatially-coupled low-density parity-check (SC-LDPC) codes, which show better asymptotic and finite-length decoding performance compared to the conventional…

Subspace codes and particularly constant dimension codes have attracted much attention in recent years due to their applications in random network coding. As a particular subclass of subspace codes, cyclic subspace codes have additional…