Related papers: Routing on trees
In this paper we model the tomography of scale free networks by studying the structure of layers around an arbitrary network node. We find, both analytically and empirically, that the distance distribution of all nodes from a specific…
A routing labeling scheme assigns a binary string, called a label, to each node in a network, and chooses a distinct port number from $\{1,\ldots,d\}$ for every edge outgoing from a node of degree $d$. Then, given the labels of $u$ and $w$…
For a graph $G$, an edge-separating (resp. vertex-separating) path system of $G$ is a family of paths in $G$ such that for any pair of edges $e_1, e_2$ (resp. pair of vertices $v_1, v_2$) of $G$ there is at least one path in the family that…
Cascade models are central to understanding, predicting, and controlling epidemic spreading and information propagation. Related optimization, including influence maximization, model parameter inference, or the development of vaccination…
Three types of explicit estimators are proposed here to estimate the loss rates of the links in a network of the tree topology. All of them are derived by the maximum likelihood principle and proved to be either asymptotic unbiased or…
This paper contains results relating currents and voltages in resistive networks to appropriate random trees or forests in those networks.
We consider a variation on Maker-Breaker games on graphs or digraphs where the edges have random costs. We assume that Maker wishes to choose the edges of a spanning tree, but wishes to minimise his cost. Meanwhile Breaker wants to make…
We study the inertia of distance matrices of weighted graphs. Our novel congruence-based proof of the inertia of weighted trees extends to a proof for the inertia of weighted unicyclic graphs whose cycle is a triangle. Partial results are…
Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…
Following up on a previous work we examine a model of transportation network in some source-sink flow paradigm subjected to growth and resource allocation. The model is inspired from plants, and we add rules and factors that are analogous…
By-tree information gathering is an essential task in precision agriculture achieved by ground mobile sensors, but it can be time- and labor-intensive. In this paper we present an algorithmic framework to perform real-time and on-the-go…
We study the height of a spanning tree $T$ of a graph $G$ obtained by starting with a single vertex of $G$ and repeatedly selecting, uniformly at random, an edge of $G$ with exactly one endpoint in $T$ and adding this edge to $T$.
We calculate the exact number of contours of size $n$ containing a fixed vertex in $d$-ary trees and provide sharp estimates for this number for more general trees. We also obtain a characterization of the locally finite trees with…
The structure of networks that provide optimal transport properties has been investigated in a variety of contexts. While many different formulations of this problem have been considered, it is recurrently found that optimal networks are…
In the broadcasting problem on trees, a $\{-1,1\}$-message originating in an unknown node is passed along the tree with a certain error probability $q$. The goal is to estimate the original message without knowing the order in which the…
Routing is one of the critical and ongoing challenges in Wireless Sensor Networks. The main challenge has always been to have a routing protocol that reduces the communication overhead, hence saving the energy of the sensors in the network.…
As well known the rotation distance D(S,T) between two binary trees S, T of n vertices is the minimum number of rotations of pairs of vertices to transform S into T. We introduce the new operation of chain rotation on a tree, involving two…
To analyze the transport of information or material from a source to every node of a network we use two quantities introduced in the study of river networks: the cost and the flow. For a network with $K$ nodes and $M$ levels, we show that…
The problem of finding a spanning forest of a graph in a distributed-processing environment is studied. If an input graph is weighted, then the goal is to find a minimum-weight spanning forest. The processors communicate by broadcasting.…
We report on a method for compiling decision trees into weighted finite-state transducers. The key assumptions are that the tree predictions specify how to rewrite symbols from an input string, and the decision at each tree node is…