In this paper we study the diculty of counting nodes in a synchronous dynamic network where nodes share the same identier, they communicate by using a broadcast with unlimited bandwidth and, at each synchronous round, network topology may change. To count in such setting, it has been shown that the presence of a leader is necessary. We focus on a particularly interesting subset of dynamic networks, namely Persistent Distance -G(PD)h, in which each node has a xed distance from the leader across rounds and such distance is at most h. In these networks the dynamic diameter D is at most 2h. We prove the number of rounds for counting inG(PD)2 is at least logarithmic with respect to the network sizejVj. Thanks to this result, we show that counting on any dynamic anonymous network with D constant w.r.t. jVj takes at least D+(log jVj) rounds where (log jVj) represents the additional cost to be payed for handling anonymity. At the best
We investigate to what extent flooding and routing is possible if the graph is allowed to change unpredictably at each time step. We study what minimal requirements are necessary so that a node may correctly flood or route a message in a network whose links may change arbitrarily at any given point, subject to the condition that the underlying graph is connected. We look at algorithmic constraints such as limited storage, no knowledge of an upper bound on the number of nodes, and no usage of identifiers. We look at flooding as well as routing to some existing specified destination and give algorithms. As the size of distributed systems keeps growing, the peer to peer communication paradigm has been identified as the key to scalability. Peer to peer overlay networks are characterized by their self-organizing capabilities, resilience to failure and fully decentralized control. In a peer to peer overlay, no entity has a global knowledge of the system. As much as this property is essential to ensure the scalability, monitoring the system under such circumstances is a complex task. Yet, estimating the size of the system is core functionality for many distributed applications to parameter setting or monitoring purposes. In this paper, we propose a comparative study between three algorithms that estimate in a fully decentralized way the size of a peer to peer overlay. Candidate approaches are generally applicable irrespective of the underlying structure of the peer to peer overlay. The paper reports the head to head comparison of estimation system size algorithms. The simulations have been conducted using the same simulation framework and inputs and highlight the differences in cost and accuracy of the estimation between the algorithms both in static and dynamic settings In this paper we investigate distributed computation in dynamic networks in which the network topology changes from round to round. We consider a worst-case model in which the communication links for each round are chosen by an adversary, and nodes do not know who their neighbors for the current round are before they broadcast their messages. The model captures mobile networks and wireless networks, in which mobility and interference render communication unpredictable. In contrast to much of the existing work on dynamic networks, we do not assume that the network eventually stops changing; we require correctness and termination even in networks that change continually. We introduce a stability property called T -interval connectivity (for T >= 1), which stipulates that for every T consecutive rounds there exists a stable connected spanning subgraph. For T = 1 this means that the graph is connected in every round, but changes arbitrarily between rounds. We show that in 1-interval connected graphs it is possible for nodes to determine the size of the network and compute any com- putable function of their initial inputs in O(n2) rounds using messages of size O(log n + d), where d is the size of the input to a single node. Further, if the graph is T-interval connected for T > 1, the computation can be sped up by a factor of T, and any function can be computed in O(n + n2 T) rounds using messages of size O(log n + d). We also give two lower bounds on the token dissemination problem, which requires the nodes to disseminate k pieces of information to all the nodes in the network. The T-interval connected dynamic graph model is a novel model, which we believe opens new avenues for research in the theory of distributed computing in wireless, mobile and dynamic networks.  This paper studies the problem of answering aggregation queries, satisfying the interval validity semantics, in a distributed system prone to continuous arrival and departure of participants. The interval validity semantics states that the query answer must be calculated considering contributions of at least all processes that remained in the distributed system for the whole query duration. Satisfying this semantics in systems experiencing unbounded churn is impossible due to the lack of connectivity and path stability between processes. This paper presents a novel architecture, namely Virtual Tree, for building and maintaining a structured overlay network with guaranteed connectivity and path stability in settings characterized by bounded churn rate. The architecture includes a simple query answering algorithm that provides interval valid answers. The overlay network generated by the Virtual Tree architecture is a tree-shaped topology with virtual nodes constituted by clusters of processes and virtual links constituted by multiple communication links connecting processes located in adjacent virtual nodes. We formally prove a bound on the churn rate for interval valid queries in a distributed system where communication latencies are bounded by a constant unknown by processes. Finally, we carry out an extensive experimental evaluation that shows the degree of robustness of the overlay network generated by the virtual tree architecture under different churn rates. This paper attempts to get at some of the fundamental properties of distributed computing by means of the following question: “How much does each processor in a network of processors need to know about its own identity, the identities of other processors, and the underlying connection network in order for the network to be able to carry out useful functions?” The approach we take is to require that the processors be designed without any knowledge (or only very broad knowledge) of the networks they are to be used in, and furthermore, that all processors with the same number of communication ports be identical. Given a particular network function, e.g., setting up a spanning tree, we ask whether processors may be designed so that when they are embedded in any connected network and started in some initial configuration, they are guaranteed to accomplish the desired function. Massive-scale self-administered networks like Peer-to-Peer and Sensor Networks have data distributed across thousands of participant hosts. These networks are highly dynamic with short-lived hosts being the norm rather than an exception. In recent years, researchers have investigated best-effort algorithms to efficiently process aggregate queries (e.g., sum, count, average, minimum and maximum) on these networks. Unfortunately, query semantics for best-effort algorithms are ill-defined, making it hard to reason about guarantees associated with the result returned. In this paper, we specify a correctness condition, Single-Site Validity, with respect to which the above algorithms are best-effort. We present a class of algorithms that guarantee validity in dynamic networks. Experiments on real-life and synthetic network topologies validate performance of our algorithms, revealing the hitherto unknown price of validity.