Related papers: On Zero-Error Capacity of Graphs with One Edge
Reasoning is a fundamental problem for computers and deeply studied in Artificial Intelligence. In this paper, we specifically focus on answering multi-hop logical queries on Knowledge Graphs (KGs). This is a complicated task because, in…
In this paper, we use the concept of colored edge graphs to model homogeneous faults in networks. We then use this model to study the minimum connectivity (and design) requirements of networks for being robust against homogeneous faults…
In this paper, we use entropy functions to characterise the set of rate-capacity tuples achievable with either zero decoding error, or vanishing decoding error, for general network coding problems. We show that when sources are colocated,…
We prove asymptotically optimal bounds on the number of edges a graph $G$ must have in order that any $r$-colouring of $E(G)$ has a colour class which contains every $D$-degenerate graph on $n$ vertices with bounded maximum degree. We also…
Graph processing is typically considered to be a memory-bound rather than compute-bound problem. One common line of thought is that more available memory bandwidth corresponds to better graph processing performance. However, in this work we…
Duan and Winter studied the one-shot zero-error classical capacity of a quantum channel assisted by quantum non-signalling correlations, and formulated this problem as a semidefinite program depending only on the Kraus operator space of the…
A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this note we give examples of class two 1-planar graphs with maximum degree six or seven.
We study natural examples of binary channels with synchronization errors. These include the duplication channel, which independently outputs a given bit once or twice, and geometric channels that repeat a given bit according to a geometric…
The paper presents a new model for single channel images low-level interpretation. The image is decomposed into a graph which captures a complete set of structural features. The description allows to accurately identify every edge location…
We propose a new channel model for channels with synchronization errors. Using this model, we give simple, non-trivial and, in some cases, tight lower bounds on the capacity for certain synchronization error channels.
IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph $G$ with $n$…
In this thesis we present several results in coding theory, concerning error-correcting codes and the Shannon capacity. 1. We give a general symmetry reduction of matrices occuring in semidefinite programs in coding theory. 2. We apply the…
The paper focuses on two problems: (i) how to orient the edges of an undirected graph in order to maximize the number of ordered vertex pairs (x,y) such that there is a directed path from x to y, and (ii) how to orient the edges so as to…
In this paper we consider the problem of secure network coding where an adversary has access to an unknown subset of links chosen from a known collection of links subsets. We study the capacity region of such networks, commonly called…
Coding schemes with extremely low computational complexity are required for particular applications, such as wireless body area networks, in which case both very high data accuracy and very low power-consumption are required features. In…
In this paper we address the problem of computing a sparse subgraph of a weighted directed graph such that the exact distances from a designated source vertex to all other vertices are preserved under bounded weight increment. Finding a…
Zero-error recovery under deterministic partial views is graph recovery for the induced confusability relation. A finite family of coordinate-subset observations determines a graph on latent states; $T$-ary exact recovery is graph…
An identifying code of a graph G is a dominating set C such that every vertex x of G is distinguished from all other vertices by the set of vertices in C that are at distance at most 1 from x. The problem of finding an identifying code of…
A secure storage code maps $K$ source symbols, each of $L_w$ bits, to $N$ coded symbols, each of $L_v$ bits, such that each coded symbol is stored in a node of a graph. Each edge of the graph is either associated with $D$ of the $K$ source…
There is a graph reduction system so that every optimal 1-planar graph can be reduced to an irreducible extended wheel graph, provided the reductions are applied such that the given graph class is preserved. A graph is optimal 1-planar if…