Mobile sensor networks are important for several strategic applications devoted to monitoring critical areas. In such hostile scenarios, sensors cannot be deployed manually and are either sent from a safe location or dropped from an aircraft. Mobile devices permit a dynamic deployment reconfiguration that improves the coverage in terms of completeness and uniformity. In this paper we propose a distributed algorithm for the autonomous deployment of mobile sensors called Push & Pull. According to our proposal, movement decisions are made by each sensor on the basis of locally available information and do not require any prior knowledge of the operating conditions or any manual tuning of key parameters. We formally prove that, when a sufficient number of sensors are available, our approach guarantees a complete and uniform coverage. Furthermore, we demonstrate that the algorithm execution always terminates preventing movement oscillations. Numerous simulations show that our algorithm reaches a complete coverage within reasonable time with moderate energy consumption, even when the target area has irregular shapes. Performance comparisons between Push & Pull and one of the most acknowledged algorithms show how the former one can efficiently reach a more uniform and complete coverage under a wide range of working scenarios

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We study the problem of the amount of information required to perform fast broadcasting in tree networks. The source located at the root of a tree has to disseminate a message to all nodes. In each round each informed node can transmit to one child. Nodes do not know the topology of the tree but an oracle knowing it can give a string of bits of advice to the source which can then pass it down the tree with the source message. The quality of a broadcasting algorithm with advice is measured by its competitive ratio: the worst case ratio, taken over n-node trees, between the time of this algorithm and the optimal broadcasting time in the given tree. Our goal is to find a trade-off between the size of advice and the best competitive ratio of a broadcasting algorithm for n-node trees. We establish such a trade-off with an approximation factor of O(n), for an arbitrarily small positive constant. This is the first problem for which a trade-off between the amount of provided information and the efficiency of the solution is shown for arbitrary size of advice.

Abstract. Topology recognition is one of the fundamental distributed tasks in networks. Each node of an anonymous network has to deterministically produce an isomorphic copy of the underlying graph, with all ports correctly marked. This task is usually unfeasible without any a priori information. Such information can be provided to nodes as advice. An oracle knowing the network can give a (possibly different) string of bits to each node, and all nodes must reconstruct the network using this advice, after a given number of rounds of communication. During each round each node can exchange arbitrary messages with all its neighbors and perform arbitrary local computations. The time of completing topology recognition is the number of rounds it takes, and the size of advice is the maximum length of a string given to nodes. We investigate tradeoffs between the time in which topology recognition is accomplished and the minimum size of advice that has to be given to nodes. We provide upper and lower bounds on the minimum size of advice that is sufficient to perform topology recognition in a given time, in the class of all graphs of size n and diameter D ≤ αn, for any constant α < 1. In most cases, our bounds are asymptotically tight. More precisely, if the allotted time is D − k, where 0 < k ≤ D, then the optimal size of advice is Θ((n 2 log n)/(D − k + 1)). If the allotted time is D, then this optimal size is Θ(n log n). If the allotted time is D + k, where 0 < k ≤ D/2, then the optimal size of advice is Θ(1 + (log n)/k). The only remaining gap between our bounds is for time D + k, where D/2 < k ≤ D. In this time interval our upper bound remains O(1 + (log n)/k), while the lower bound (that holds for any time) is 1. This leaves a gap if D ∈ o(log n). Finally, we show that for time 2D + 1, one bit of advice is both necessary and sufficient. Our results show how sensitive is the minimum size of advice to the time allowed for topology recognition: allowing just one round more, from D to D + 1, decreases exponentially the advice needed to accomplish this task.

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In this paper we propose an algorithm for the autonomous deployment of mobile sensors over critical target areas where sensors cannot be deployed manually. The application of our approach does not require prior knowledge of the working scenario nor any manual tuning of key parameters. Our algorithm is completely distributed and sensors make movement decisions on the basis of locally available information. We prove that our approach guarantees a complete coverage, provided that a sufficient number of sensors are available. Furthermore, we demonstrate that the algorithm execution always terminates preventing movement oscillations. We compare our proposal with one of the most acknowledged algorithms by means of extensive simulations, showing that our algorithm reaches a complete and more uniform coverage under a wide range of operating conditions.

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We study the time needed for deterministic leader election in the LOCAL model, where in every round a node can exchange any messages with its neighbors and perform any local computations. The topology of the network is unknown and nodes are unlabeled, but ports at each node have arbitrary fixed labelings which, together with the topology of the network, can create asymmetries to be exploited in leader election. We consider two versions of the leader election problem: strong LE in which exactly one leader has to be elected, if this is possible, while all nodes must terminate declaring that leader election is impossible otherwise, and weak LE, which differs from strong LE in that no requirement on the behavior of nodes is imposed, if leader election is impossible. We show that the time of leader election depends on three parameters of the network: its diameter D, its size n, and its level of symmetry λ, which, when leader election is feasible, is the smallest depth at which some node has a unique view of the network. It also depends on the knowledge by the nodes, or lack of it, of parameters D and n.