Finding routes in anonymous sensor networks

We consider networks of anonymous sensors and address the problem of constructing routes for the delivery of information from a group of sensors in response to a query by a sink. In order to circumvent the restrictions imposed by anonymity, we rely on using the power level perceived by the sensors in the query from the sink. We introduce a simple distributed algorithm to achieve the building of routes to the sink and evaluate its performance by means of simulations

Multicast Network Design Game on a Ring

In this paper we study quality measures of different solution concepts for the multicast network design game on a ring topology. We recall from the literature a lower bound of 4/3 and prove a matching upper bound for the price of stability, which is the ratio of the social costs of a best Nash equilibrium and of a general optimum. Therefore, we answer an open question posed by Fanelli et al. in [12]. We prove an upper bound of 2 for the ratio of the costs of a potential optimizer and of an optimum, provide a construction of a lower bound, and give a computer-assisted argument that it reaches $2$ for any precision. We then turn our attention to players arriving one by one and playing myopically their best response. We provide matching lower and upper bounds of 2 for the myopic sequential price of anarchy (achieved for a worst-case order of the arrival of the players). We then initiate the study of myopic sequential price of stability and for the multicast game on the ring we construct a lower bound of 4/3, and provide an upper bound of 26/19. To the end, we conjecture and argue that the right answer is 4/3.Comment: 12 pages, 4 figure

Distributed anonymous function computation in information fusion and multiagent systems

We propose a model for deterministic distributed function computation by a network of identical and anonymous nodes, with bounded computation and storage capabilities that do not scale with the network size. Our goal is to characterize the class of functions that can be computed within this model. In our main result, we exhibit a class of non-computable functions, and prove that every function outside this class can at least be approximated. The problem of computing averages in a distributed manner plays a central role in our development

Topology recognition with advice

In topology recognition, 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 $D\le \alpha n$, for any constant $\alpha< 1$. In most cases, our bounds are asymptotically tight

Computing on Anonymous Quantum Network

This paper considers distributed computing on an anonymous quantum network, a network in which no party has a unique identifier and quantum communication and computation are available. It is proved that the leader election problem can exactly (i.e., without error in bounded time) be solved with at most the same complexity up to a constant factor as that of exactly computing symmetric functions (without intermediate measurements for a distributed and superposed input), if the number of parties is given to every party. A corollary of this result is a more efficient quantum leader election algorithm than existing ones: the new quantum algorithm runs in O(n) rounds with bit complexity O(mn^2), on an anonymous quantum network with n parties and m communication links. Another corollary is the first quantum algorithm that exactly computes any computable Boolean function with round complexity O(n) and with smaller bit complexity than that of existing classical algorithms in the worst case over all (computable) Boolean functions and network topologies. More generally, any n-qubit state can be shared with that complexity on an anonymous quantum network with n parties.Comment: 25 page

Leader Election for Anonymous Asynchronous Agents in Arbitrary Networks

We study the problem of leader election among mobile agents operating in an arbitrary network modeled as an undirected graph. Nodes of the network are unlabeled and all agents are identical. Hence the only way to elect a leader among agents is by exploiting asymmetries in their initial positions in the graph. Agents do not know the graph or their positions in it, hence they must gain this knowledge by navigating in the graph and share it with other agents to accomplish leader election. This can be done using meetings of agents, which is difficult because of their asynchronous nature: an adversary has total control over the speed of agents. When can a leader be elected in this adversarial scenario and how to do it? We give a complete answer to this question by characterizing all initial configurations for which leader election is possible and by constructing an algorithm that accomplishes leader election for all configurations for which this can be done

Distributed anonymous discrete function computation

We propose a model for deterministic distributed function computation by a network of identical and anonymous nodes. In this model, each node has bounded computation and storage capabilities that do not grow with the network size. Furthermore, each node only knows its neighbors, not the entire graph. Our goal is to characterize the class of functions that can be computed within this model. In our main result, we provide a necessary condition for computability which we show to be nearly sufficient, in the sense that every function that satisfies this condition can at least be approximated. The problem of computing suitably rounded averages in a distributed manner plays a central role in our development; we provide an algorithm that solves it in time that grows quadratically with the size of the network