Related papers: Rate-distance tradeoff for codes above graph capac…
Structure and dynamics of complex networks usually deal with degree distributions, clustering, shortest path lengths and other graph properties. Although these concepts have been analysed for graphs on abstract spaces, many networks happen…
We derive a single-letter upper bound to the mismatched-decoding capacity for discrete memoryless channels. The bound is expressed as the mutual information of a transformation of the channel, such that a maximum-likelihood decoding error…
We study common randomness generation problems where $n$ players aim to generate same sequences of random coin flips where some subsets of the players share an independent common coin which can be tossed multiple times, and there is a…
We consider the problem of broadcast with common messages, and focus on the case that the common message rate $R_{\mathcal{A}}$, i.e., the rate of the message intended for all the receivers in the set $\mathcal{A}$, is the same for all the…
In this second part of our multi-part papers, the information flow in degraded interference networks is studied. A full characterization of the sum-rate capacity for the degraded networks with any possible configuration is established. It…
Explicit characterization and computation of the multi-source network coding capacity region (or even bounds) is long standing open problem. In fact, finding the capacity region requires determination of the set of all entropic vectors…
We display several examples of how fields with different limiting velocities (the "speed of light") at a high energy scale can nevertheless have a common limiting velocity at low energies due to the effects of interactions. We evaluate the…
We study the relation between the growth rate of a graph property and the entropy of the graph limits that arise from graphs with that property. In particular, for hereditary classes we obtain a new description of the colouring number,…
We define a distance metric between partitions of a graph using machinery from optimal transport. Our metric is built from a linear assignment problem that matches partition components, with assignment cost proportional to transport…
Many load balancing problems that arise in scientific computing applications ask to partition a graph with weights on the vertices and costs on the edges into a given number of almost equally-weighted parts such that the maximum boundary…
A forcing set for a perfect matching of a graph is defined as a subset of the edges of that perfect matching such that there exists a unique perfect matching containing it. A complete forcing set for a graph is a subset of its edges, such…
A sequence of graphs with diverging number of nodes is a dense graph sequence if the number of edges grows approximately as for complete graphs. To each such sequence a function, called graphon, can be associated, which contains information…
The probabilistic graphs framework models the uncertainty inherent in real-world domains by means of probabilistic edges whose value quantifies the likelihood of the edge existence or the strength of the link it represents. The goal of this…
The Bandwidth Problem seeks for a simultaneous permutation of the rows and columns of the adjacency matrix of a graph such that all nonzero entries are as close as possible to the main diagonal. This work focuses on investigating novel…
Many physical systems -- such as optical waveguide lattices and dense neuronal or vascular networks -- can be modeled by metric graphs, where slender "wires" (edges) support wave or diffusion equations subject to Kirchhoff conditions at the…
This paper studies the capacity of a class of discrete memoryless interference channels where interference is defined analogous to that of Gaussian interference channel with one-sided weak interference. The sum-rate capacity of this class…
We consider the capacity problem (or, the single slot scheduling problem) in wireless networks. Our goal is to maximize the number of successful connections in arbitrary wireless networks where a transmission is successful only if the…
We consider a class of growing random graphs obtained by creating vertices sequentially one by one: at each step, we choose uniformly the neighbours of the newly created vertex; its degree is a random variable with a fixed but arbitrary…
Throttling in graphs optimizes a sum or product of resources used, such as the number of vertices in an initial set, and time required, such as the propagation time, to complete a given task. We introduce a new technique to establish sharp…
We study the problem of communicating over a discrete memoryless two-way channel using non-adaptive schemes, under a zero probability of error criterion. We derive single-letter inner and outer bounds for the zero-error capacity region,…