Related papers: Error Probability Bounds for M-ary Relay Trees
We consider three different schemes for signal routing on a tree. The vertices of the tree represent transceivers that can transmit and receive signals, and are equipped with i.i.d. weights representing the strength of the transceivers. The…
Neutral macroevolutionary models, such as the Yule model, give rise to a probability distribution on the set of discrete rooted binary trees over a given leaf set. Such models can provide a signal as to the approximate location of the root…
The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…
Solving fastest distributed consensus averaging problem (i.e., finding weights on the edges to minimize the second-largest eigenvalue modulus of the weight matrix) over networks with different topologies is one of the primary areas of…
We revisit the problem of broadcasting on $d$-ary trees: starting from a Bernoulli$(1/2)$ random variable $X_0$ at a root vertex, each vertex forwards its value across binary symmetric channels $\mathrm{BSC}_\delta$ to $d$ descendants. The…
We investigate the size of vertex confidence sets for including part of (or the entirety of) the seed in seeded uniform attachment trees, given knowledge of some of the seed's properties, and with a prescribed probability of failure. We…
We consider root-finding algorithms for random rooted trees grown by uniform attachment. Given an unlabeled copy of the tree and a target accuracy $\varepsilon > 0$, such an algorithm outputs a set of nodes that contains the root with…
In this paper, we study the problem of coordinating two nodes which can only exchange information via a relay at limited rates. The nodes are allowed to do a two-round interactive two-way communication with the relay, after which they…
In this article, we calculate the mean throughput, number of collisions, successes, and idle slots for random tree algorithms with successive interference cancellation. Except for the case of the throughput for the binary tree, all the…
We extend some results of Itai Benjamini and Yuri Lima (see \href{http://arxiv.org/pdf/1305.2610.pdf}{\cite{Benjamini}}). In this paper they consider a binary tree $\mathbb T_n$ of height $n$, each leaf is either infected by one of $k$…
We consider the discrete memoryless symmetric primitive relay channel, where, a source $X$ wants to send information to a destination $Y$ with the help of a relay $Z$ and the relay can communicate to the destination via an error-free…
Computing and storing probabilities is a hard problem as soon as one has to deal with complex distributions over multiple random variables. The problem of efficient representation of probability distributions is central in term of…
Several real-world and abstract structures and systems are characterized by marked hierarchy to the point of being expressed as trees. Because the study of these entities often involves sampling (or discovering) the tree nodes in a specific…
We study the arboricity A and the maximum number T of edge-disjoint spanning trees of the Erdos-Renyi random graph G(n,p). For all p(n) in [0,1], we show that, with high probability, T is precisely the minimum between delta and…
Imitating a recently introduced invariant of trees, we initiate the study of the inducibility of $d$-ary trees (rooted trees whose vertex outdegrees are bounded from above by $d\geq 2$) with a given number of leaves. We determine the exact…
A Multinomial Processing Tree (MPT) is a directed tree with a probability associated with each arc. Here we consider an additional parameter associated with each arc, a measure such as the time required to select the arc. MPTs are often…
We consider a broadcasting problem on a tree where a binary digit (e.g., a spin or a nucleotide's purine/pyrimidine type) is propagated from the root to the leaves through symmetric noisy channels on the edges that randomly flip the state…
This paper presents two-hop relay gain-scheduling control in a Wireless Sensor Network to estimate a static target prior characterized by Gaussian probability distribution. The target is observed by a network of linear sensors, whose…
Cascaded binary hypothesis testing is studied in this paper with two decision centers at the relay and the receiver. All terminals have their own observations, where we assume that the observations at the transmitter, the relay, and the…
Given a rooted tree and a ranking of its leaves, what is the minimum number of inversions of the leaves that can be attained by ordering the tree? This variation of the problem of counting inversions in arrays originated in mathematical…