Related papers: Reduction and Fixed Points of Boolean Networks and…
We consider a single-source, multiple-relay, single-destination lossy network employing Random Linear Network coding at all transmitting nodes. We address the problem of calculating the probability of successful decoding at the destination…
Motivated by the increasing need to understand the distributed algorithmic foundations of large-scale graph computations, we study some fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…
We study index-coding problems (one sender broadcasting messages to multiple receivers) where each message is requested by one receiver, and each receiver may know some messages a priori. This type of index-coding problems can be fully…
We consider the level of information security provided by random linear network coding in network scenarios in which all nodes comply with the communication protocols yet are assumed to be potential eavesdroppers (i.e. "nice but curious").…
To address growth challenges facing large Data Centers and supercomputing clusters a new construction is presented for scalable, high throughput, low latency networks. The resulting networks require 1.5-5 times fewer switches, 2-6 times…
To each Boolean function F from {0,1}^n to itself and each point x in {0,1}^n, we associate the signed directed graph G_F(x) of order n that contains a positive (resp. negative) arc from j to i if the partial derivative of f_i with respect…
The simple greedy algorithm to find a maximal independent set of a graph can be viewed as a sequential update of a Boolean network, where the update function at each vertex is the conjunction of all the negated variables in its…
The multicut problem is an NP-hard combinatorial optimization problem with diverse applications in fields such as bioinformatics, data mining and computer vision. Graph neural networks have been defined for the multicut problem but can be…
Message passing graph neural networks are widely used for learning on graphs, yet their expressive power is limited by the one-dimensional Weisfeiler-Lehman test and can fail to distinguish structurally different nodes. We provide rigorous…
A linear programming (LP) based framework is presented for obtaining converses for finite blocklength lossy joint source-channel coding problems. The framework applies for any loss criterion, generalizes certain previously known converses,…
We prove several new tight distributed lower bounds for classic symmetry breaking graph problems. As a basic tool, we first provide a new insightful proof that any deterministic distributed algorithm that computes a $\Delta$-coloring on…
Random linear network coding is a particularly decentralized approach to the multicast problem. Use of random network codes introduces a non-zero probability however that some sinks will not be able to successfully decode the required…
This paper considers vector network coding solutions based on rank-metric codes and subspace codes. The main result of this paper is that vector solutions can significantly reduce the required alphabet size compared to the optimal scalar…
The edge removal problem studies the loss in network coding rates that results when a network communication edge is removed from a given network. It is known, for example, that in networks restricted to linear coding schemes and networks…
The problem of computing a linear combination of sources over a multiple access channel is studied. Inner and outer bounds on the optimal tradeoff between the communication rates are established when encoding is restricted to random…
Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. The topologies of random Boolean networks with one input per…
We consider a two-unicast-$Z$ network over a directed acyclic graph of unit capacitated edges; the two-unicast-$Z$ network is a special case of two-unicast networks where one of the destinations has apriori side information of the unwanted…
Graph colorings have been of interest to mathematicians for a long time, but relatively recently, social scientists have also found them to be interesting tools for studying group behavior. In the last 20 years, scientists have begun to…
We are interested in assigning a pre-specified number of nodes as leaders in order to minimize the mean-square deviation from consensus in stochastically forced networks. This problem arises in several applications including control of…
In network communications, information transmission often encounters wiretapping attacks. Secure network coding is introduced to prevent information from being leaked to adversaries. The investigation of performance bounds on the numbers of…