Angelo Monti

Distributed broadcast in radio networks of unknown topology

A multi-hop synchronous radio network is said to be unknown if the nodes have no knowledge of the topology. A basic task in radio network is that of broadcasting a message (created by a fixed source node) to all nodes of the network. Typical operations in real-life radio networks is the multi-broadcast that consists in performing a set of r independent broadcasts. The study of broadcast operations on unknown radio network is started by the seminal paper of Bar-Yehuda et al. [J. Comput. System Sci. 45 (1992) 104] and has been the subject of several recent works.In this paper, we study the completion and the termination time of distributed protocols for both the (single) broadcast and the multi-broadcast operations on unknown networks as functions of the number of nodes n, the maximum eccentricity D, the maximum in-degree Δ, and the congestion c of the networks. We establish new connections between these operations and some combinatorial concepts, such as selective families, strongly selective families (also known as superimposed codes), and pairwise r-different families. Such connections, combined with a set of new lower and upper bounds on the size of the above families, allow us to derive new lower bounds and new distributed protocols for the broadcast and multi-broadcast operations. In particular, our upper bounds are almost tight and strongly improve over the previous bounds for a large class of networks.

Flooding time in edge-Markovian dynamic graphs

We introduce stochastic time-dependency in evolving graphs: starting from an arbitrary initial edge probability distribution, at every time step, every edge changes its state (existing or not) according to a two-state Markovian process with probabilities p (edge birth-rate) and q (edge death-rate). If an edge exists at time t then, at time t+1, it dies with probability q. If instead the edge does not exist at time t, then it will come into existence at time t+1 with probability p. Such evolving graph model is a wide generalization of time-independent dynamic random graphs [6] and will be called edge-Markovian dynamic graphs. We investigate the speed of information dissemination in such dynamic graphs. We provide nearly tight bounds (which in fact turn out to be tight for a wide range of probabilities p and q) on the completion time of the flooding mechanism aiming to broadcast a piece of information from a source node to all nodes. In particular, we provide: i) A tight characterization of the class of edge-Markovian dynamic graphs where flooding time is constant and, thus, it does not asymptotically depend on the initial probability distribution. ii) A tight characterization of the class of edge-Markovian dynamic graphs where flooding time does not asymptotically depend on the edge death-rate q.

Information spreading in stationary Markovian evolving graphs

Markovian evolving graphs are dynamic-graph models where the links among a fixed set of nodes change during time according to an arbitrary Markovian rule. They are extremely general and they can well describe important dynamic-network scenarios. We study the speed of information spreading in the stationary phase by analyzing the completion time of the flooding mechanism. We prove a general theorem that establishes an upper bound on flooding time in any stationary Markovian evolving graph in terms of its node-expansion properties. We apply our theorem in two natural and relevant cases of such dynamic graphs. Geometric Markovian evolving graphs where the Markovian behaviour is yielded by n mobile radio stations, with fixed transmission radius, that perform independent random walks over a square region of the plane. Edge-Markovian evolving graphs where the probability of existence of any edge at time t depends on the existence (or not) of the same edge at time t-1. In both cases, the obtained upper bounds hold with high probability and they are nearly tight. In fact, they turn out to be tight for a large range of the values of the input parameters. As for geometric Markovian evolving graphs, our result represents the first analytical upper bound for flooding time on a class of concrete mobile networks.

Round Robin is optimal for fault-tolerant broadcasting on wireless networks

We study the completion time of broadcast operations on static ad hoc wireless networks in presence of unpredictable and dynamical faults.Concerning oblivious fault-tolerant distributed protocols, we provide an Ω(Dn) lower bound where n is the number of nodes of the network and D is the source eccentricity in the fault-free part of the network. Rather surprisingly, this lower bound implies that the simple Round Robin protocol, working in O(Dn) time, is an optimal fault-tolerant oblivious protocol. Then, we demonstrate that networks of o(n/log n) maximum in-degree admit faster oblivious protocols. Indeed, we derive an oblivious protocol having O(D min{n, Δ log n}) completion time on any network of maximum in-degree Δ.Finally, we address the question whether adaptive protocols can be faster than oblivious ones. We show that the answer is negative at least in the general setting: we indeed prove an Ω(Dn) lower bound when D = Θ(√n). This clearly implies that no (adaptive) protocol can achieve, in general, o(Dn) completion time.

Flooding Time of Edge-Markovian Evolving Graphs

=1We introduce stochastic time-dependency in evolving graphs: starting from an initial graph, at every time step, every edge changes its state (existing or not) according to a two-state Markovian process with probabilities

Efficient Algorithms for Low-Energy Bounded-Hop Broadcast in Ad-Hoc Wireless Networks

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A linear-time algorithm for the feasibility of pebble motion on trees

(edge birth-rate) and

Information Spreading in Stationary Markovian Evolving Graphs

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Broadcasting in dynamic radio networks

(edge death-rate). If an edge exists at time

Communication in dynamic radio networks

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