Emanuele G. Fusco

In this paper we deal with k-arch graphs, a superclass of trees and k-trees. We give a recursive function counting the number of labeled k-arch graphs. Our result relies on a generalization of the well-known Prufer code for labeled trees. In order to guarantee the generalized code to be a bijection, we characterize the valid code strings. A previous attempt

We consider static ad-hoc wireless networks where nodes have the same initial battery charge and they may dynamically change their transmission range at every time slot. When a node v transmits with range r(v), its battery charge is decreased by β × r(v)2 where β > 0 is a fixed constant. The goal is to provide a range assignment schedule that maximizes the number of broadcast operations from a given source (this number is denoted as the length of the schedule). This maximization problem, denoted as MAX LIFETIME, is known to be NP-hard and the best algorithm yields worst-case approximation ratio Θ(log n), where n is the number of nodes of the network [5]. We consider random geometric instances formed by selecting n points independently and uniformly at random from a square of side length √n in the Euclidean plane. We first present an efficient algorithm that constructs a range assignment schedule having length, with high probability, not smaller than 1/12 of the optimum. We then d...

ABSTRACT We consider the task of learning a ring in a distributed way: each node of an unknown ring has to construct a labeled map of it. Nodes are equipped with unique labels. Communication proceeds in synchronous rounds. In every round every node can send arbitrary messages to its neighbors and perform arbitrary local computations. We study tradeoffs between the time (number of rounds) and the cost (number of messages) of completing this task in a deterministic way: for a given time T we seek bounds on the smallest number of messages needed for learning the ring in time T. Our bounds depend on the diameter D of the ring and on the delayθ=T−D above the least possible time D in which this task can be performed. We prove a lower bound Ω(D2/θ) on the number of messages used by any algorithm with delay θ, and we design a class of algorithms that give an almost matching upper bound: for any positive constant 0<ε<1 there is an algorithm working with delay θ≤D and using O(D2 (log*D)/θ1−ε) messages.

... Tiziana Calamoneri1, Emanuele G. Fusco1, Anil M. Shende2, and Sunil M. Shende3 ... At each instant in time (in a given time period), the set of objects participating in the phenomenon, together with their attribute values (such as speed, spin, etc.) at that time, completely ...

Abstract—We consider static ad hoc wireless networks whose nodes, equipped with the same initial battery charge, may dynamically change their transmission range. When a node $v$ transmits with range $r(v)$ , its battery charge is decreased by $\beta \; r(v)^2$ , where $\beta >0$ ...

Abstract We consider asynchronous deterministic broadcasting in radio networks. An execution of a broadcasting protocol is a series of events, each of which consists of simultaneous transmitting or delivering of messages. The aim is to transmit the source message to all nodes of the network. If two messages are delivered simultaneously to a node, a collision occurs and this node