Related papers: On network coding for sum-networks
In an acyclic multicast network, it is well known that a linear network coding solution over GF($q$) exists when $q$ is sufficiently large. In particular, for each prime power $q$ no smaller than the number of receivers, a linear solution…
In this short note we provide a proof of boundedness of solutions for a network system composed of heterogeneous nonlinear autonomous systems interconnected over a directed graph. The sole assumptions imposed are that the systems are…
Link and node failures are common two fundamental problems that affect operational networks. Hence, protection of communication networks is essential to increase their reliability, performance, and operations. Much research work has been…
A rooted acyclic digraph N with labelled leaves displays a tree T when there exists a way to select a unique parent of each hybrid vertex resulting in the tree T. Let Tr(N) denote the set of all trees displayed by the network N. In general,…
There exists an injective, information-preserving function that maps a semantic network (i.e a directed labeled network) to a directed network (i.e. a directed unlabeled network). The edge label in the semantic network is represented as a…
The network communication scenario where one or more receivers request all the information transmitted by different sources is considered. We introduce distributed polynomial-time network codes in the presence of malicious nodes. Our codes…
We study the set of networks, which consist of sources, sinks and neutral points, bijective to the permutations. The set of directed edges, which characterizes a network, is constructed from a polyomino or a Rothe diagram of a permutation…
Network coding is studied when an adversary controls a subset of nodes in the network of limited quantity but unknown location. This problem is shown to be more difficult than when the adversary controls a given number of edges in the…
Using closure concepts, we show that within every undirected network, or graph, there is a unique irreducible subgraph which we call its "spine". The chordless cycles which comprise this irreducible core effectively characterize the…
We study upper bounds on the sum-rate of multiple-unicasts. We approximate the Generalized Network Sharing Bound (GNS cut) of the multiple-unicasts network coding problem with $k$ independent sources. Our approximation algorithm runs in…
Bayesian networks are directed acyclic graphs representing independence relationships among a set of random variables. A random variable can be regarded as a set of exhaustive and mutually exclusive propositions. We argue that there are…
Consensus is a common method for computing a function of the data distributed among the nodes of a network. Of particular interest is distributed average consensus, whereby the nodes iteratively compute the sample average of the data stored…
Parties connected to independent sources through a network can generate correlations among themselves. Notably, the space of feasible correlations for a given network, depends on the physical nature of the sources and the measurements…
We introduce linear network coding on parallel architecture for multi-source finite acyclic network. In this problem, different messages in diverse time periods are broadcast and every nonsource node in the network decodes and encodes the…
We consider the problem of computing an $(s,d)$-hypernetwork in an acyclic F-hypergraph. This is a fundamental computational problem arising in directed hypergraphs, and is a foundational step in tackling problems of reachability and…
We consider a network coding setting where some of the messages and edges have fixed alphabet sizes, that do not change when we increase the common alphabet size of the rest of the messages and edges. We prove that the problem of deciding…
In this paper we investigate formal verification problems for Neural Network computations. Of central importance will be various robustness and minimization problems such as: Given symbolic specifications of allowed inputs and outputs in…
We study the question of reconstructing a weighted, directed network up to isomorphism from its motifs. In order to tackle this question we first relax the usual (strong) notion of graph isomorphism to obtain a relaxation that we call weak…
The linear deterministic model has been used recently to get a first order understanding of many wireless communication network problems. In many of these cases, it has been pointed out that the capacity regions of the network and its…
Data vectors generalise finite multisets: they are finitely supported functions into a commutative monoid. We study the question if a given data vector can be expressed as a finite sum of others, only assuming that 1) the domain is…