We introduce projection analysis – a new technique to analyze the stopping time of gossip protocols that are based on random linear network coding (RLNC). Projection analysis drastically simplifies, extends and strengthens previous results. We analyze RLNC gossip in a general framework for network and communication models that encompasses and unifies the models used previously in this context. We show, in most settings for the first time, that the RLNC gossip converges with high probability in optimal time. Most stopping times are of the form O(k + T), where k is the number of messages to be distributed and T is the time it takes to disseminate one message. This means RLNC gossip achieves “perfect pipelining”. Our analysis directly extends to highly dynamic networks in which the topology can change completely at any time. This remains true, even if the network dynamics are controlled by a fully adaptive adversary that knows the complete network state. Virtually nothing besides simple O(kT) sequential flooding protocols was previously known for such a setting. While RLNC gossip works in this wide variety of networks our analysis remains the same and extremely simple. This contrasts with more complex proofs that were put forward to give less strong results for various special cases.

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The Minimum Spanning Tree (MST) problem is an important and commonly occurring primitive in the design and operation of data and communication networks. While there are distributed algorithms for the MST problem, these algorithms require relatively large number of messages and time, and are fairly involved, require synchronization and a lot of book keeping; this makes these algorithms impractical for resource-constrained networks such as ad hoc wireless sensor networks. In such networks, a sensor has very limited power, and any algorithm needs to be simple, local, and energy efficient for being practical. Motivated by these considerations, we design and analyze a class of simple and local distributed algorithms called Nearest Neighbor Tree (NNT) algorithms for energy-efficient construction of MSTs in a wireless ad hoc setting. We assume that the nodes are uniformly distributed in a unit square and show provable bounds on the performance with respect to both the quality of the spanning tree produced and the energy needed to construct them. In particular, we show that NNT produces a close approximation to the MST, and they can be maintained dynamically with polylogarithmic number of rearrangements under node insertions/deletions. We also perform extensive simulations of our algorithms. We tested our algorithms on both uniformly random distributions of nodes, and on a realistic distributions of nodes in an urban setting. Simulations validate

Abstract—Consider a network of, say, sensors, or P2P nodes, or bluetooth-enabled cell-phones, where nodes transmit information to each other and where links and nodes can go up or down. Consider also a ‘datum’, that is, a piece of information, like a report of an emergency condition in a sensor network, a national traditional song, or a mobile phone virus. How often should nodes transmit the datum to each other, so that the datum can survive (or, in the virus case, under what conditions will the virus die out)? Clearly, the link and node fault probabilities are important — what else is needed to ascertain the survivability of the datum? We propose and solve the problem using non-linear dynamical systems and fixed point stability theorems. We provide a closedform formula that, surprisingly, depends on only one additional parameter, the largest eigenvalue of the connectivity matrix. We illustrate the accuracy of our analysis on realistic and real settings, like mote sensor networks from Intel and MIT, as well as Gnutella and P2P networks. I.

Abstract. This paper is about consensus solutions optimized simultaneously for the time and communication complexities. Synchronous message passing with processors prone to crashes is the computing environment. The number f of crashes can be arbitrary as long as it is smaller than the number n of processors in the system. As a building block to our consensus solutions, we consider the gossiping problem in which processors have input rumors and the goal of every processor is to learn all the rumors of the processors that have not crashed. We show that gossiping can be achieved by a deterministic algorithm working in O(log 3 n) time and sending O(n log 4 n) point-to-point messages. These results improve upon the best previously known deterministic solution of gossiping that operated in O(log 2 n) time and generated O(n 1+ε) messages, for any constant ε> 0. The efficient gossiping algorithm is applied to the problem of reaching consensus. In the Consensus problem, each processor starts with its input value and the goal is to have all processors agree on exactly one value among the inputs. First we develop a deterministic algorithm solving Consensus in O(n) time while sending O(n log 5 n) messages. The best previously known algorithms solving Consensus in O(n) time had the message complexity bounded by O(n 1+ε), for any constant ε> 0. Next we improve the Consensus solution so that it is early stopping, which means that it terminates in O(f + 1) time, where f is the number of crashes in an execution, while preserving the message complexity O(n log 5 n). 1

We present a method for using real world mobility traces to identify tractable theoretical models for the study of distributed algorithms in mobile networks. We validate the method by deriving a vehicular ad hoc network model from a large corpus of position data generated by Boston-area taxicabs. Unlike previous work, our model does not assume global connectivity or eventual stability; it instead assumes only that some subset of processes are connected through transient paths (e.g., paths that exist over time). We use this model to study the problem of prioritized gossip, in which processes attempt to disseminate messages of different priority. Specifically, we present CabChat, a distributed prioritized gossip algorithm that leverages an interesting connection to the classic Tower of Hanoi problem to schedule the broadcast of packets of different priorities. Whereas previous studies of gossip leverage strong connectivity or stabilization assumptions to prove the time complexity of global termination, in our model, with its weak assumptions, we instead analyze CabChat with respect to its ability to deliver a high proportion of high priority messages over the transient paths that happen to exist in a given execution.

This paper investigates how the principles underlying online social network services could be used to take advantage of node mobility in an opportunistic manner. As an example, we show how to take advantage of opportunistic contacts between mobile phones that run an online social network service. Our model includes static nodes, and mobile nodes which follow random walks. As in an online network service, we assume that each node can only communicate with a small subset of others nodes (called its mates) in addition to its geographical neighbors. Here we prove that, in such context, a simple connection scheme enables to execute sophisticated tasks (e.g., routing) and mechanisms (e.g., spatial gossip), while using only opportunistic communication and communication between mates. In other words, our results show that future online social networks can exploit mobility as long as they forget connections appropriately.

Many distributed applications are employing gossip-based message dissemination, where the burden of message distribution is placed on recipient nodes. We are concerned with emerg-ing systems (e.g., peer-to-peer designs for RSS dissemination, queries and code propagation in stationary wireless sensor network systems) that are multiple-source, multiple-recipient systems, where each recipient node is interested in all the streams. Default gossip-based ap-proaches tend to treat each stream independently of the others, overloading each node with message overhead summed from all streams. In this thesis, we apply intelligent schedul-ing strategies for gossip forwarding, effectively piggybacking streams atop one another, to address this significant message overhead. Our problem formulation introduces a new con-cept called the “semblance graph” among gossip streams, based on streams’ frequencies. Our solution consists of two new heuristic algorithms to solve the semblance graph prob-lem. Both heuristics are inspired by Minimum Spanning Tree algorithms. Our semblance graph evaluation shows that the performance of these two heuristics is within 3.5 % of the optimal solution. Our distributed systems simulations show that these scheduling strategies

Abstract: Peers in a peer-to-peer (P2P) system have widely differing performance characteristics and are subject to time-varying workloads. However, once a peer has been deployed, reconfiguring it is difficult, if not impossible. It is, therefore, important for a peer to adapt its behavior to variations in network and workload characteristics. In this paper, we present adaptive mechanisms for two specific problems in peerto-peer search systems: efficient flooding in unstructured P2P systems and search algorithm selection in hybrid P2P systems. Both algorithms use a mathematical model to predict an expected result, compare the actual result to the prediction, and feed back the error to adapt future responses. This allows the system to automatically adapt to changes in the operating environment. Synthetic and trace-driven simulations show substantial gain due to these adaptive techniques. Adaptive flooding provides the same recall as dynamic querying, but with 22 % lower bandwidth cost. Similarly, compared to a non-adaptive hybrid approach our adaptive algorithm can achieve a 51 % smaller last response time, and 1.9 times smaller bandwidth use, with no loss in recall. Our algorithms scale well, with only a 3-9 % degradation in performance with a 3x increase in system size. These lead us to conclude that adaptation can greatly improve performance of both existing and future peer-to-peer systems. I.

Abstract. We propose a dynamic process for network evolution, aiming at explaining the emergence of the small world phenomenon, i.e., the statistical observation that any pair of individuals are linked by a short chain of acquaintances computable by a simple decentralized routing algorithm, known as greedy routing. Our model is based on the combination of two dynamics: a random walk (spatial) process, and an harmonic forgetting (temporal) process. Both processes reflect natural behaviors of the individuals, viewed as nodes in the network of inter-individual acquaintances. We prove that, in k-dimensional lattices, the combination of these two processes generates long-range links mutually independently distributed as a k-harmonic distribution. We analyze the performances of greedy routing at the stationary regime of our process, and prove that the expected number of steps for routing from any source to any target in any multidimensional lattice is a polylogarithmic function of the distance between the two nodes in the lattice. Up to our knowledge, these results are the first formal proof that navigability in small worlds can emerge from a dynamic process for network evolution. Our dynamica process can find practical applications to the design of spatial gossip and resource location protocols.