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.

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.

Abstract. We study problems of data aggregation, such as approximate counting and computing the minimum input value, in synchronous directed networks with bounded message bandwidthB = Ω(logn). In undirected networks of diameter D, many such problems can easily be solved in O(D) rounds, using O(logn)size messages. We show that for directed networks this is not the case: when the bandwidth B is small, several classical data aggregation problems have a time complexity that depends polynomially on the size of the network, even when the diameter of the network is constant. We show that computing anǫ-approximation to the size n of the network requires Ω(min { n,1/ǫ 2} /B) rounds, even in networks of diameter 2. We also show that computing a sensitive function (e.g., minimum and maximum) requires Ω ( √ n/B) rounds in networks of diameter 2, provided that the diameter is not known in advance to be o ( √ n/B). Our lower bounds are established by reduction from several well-known problems in communication complexity. On the positive side, we give a nearly optimal Õ(D+ √ n/B)-round algorithm for computing simple sensitive functions using messages of size B = Ω(logN), where N is a loose upper bound on the size of the network and D is the diameter. 1

We study several variants of coordinated consensus in dynamic networks. We assume a synchronous model, where the communication graph for each round is chosen by a worst-case adversary. The network topology is always connected, but can change completely from one round to the next. The model captures mobile and wireless networks, where communication can be unpredictable. In this setting we study the fundamental problems of eventual, simultaneous, and ∆-coordinated consensus, as well as their relationship to other distributed problems, such as determining the size of the network. We show that in the absence of a good initial upper bound on the size of the network, eventual consensus is as hard as computing deterministic functions of the input, e.g., the minimum or maximum of inputs to the nodes. We also give an algorithm for computing such functions that is optimal in every execution. Next, we show that simultaneous consensus can never be achieved in less than n−1 rounds in any execution, where n is the size of the network; consequently, simultaneous consensus is as hard as computing an upper bound on the number of nodes in the network. For ∆-coordinated consensus, we show that if the ratio between nodes with input 0 and input 1 is bounded away from 1, it is possible to decide in timen−Θ ( √ n∆), where∆bounds the time from the first decision until all nodes decide. If the dynamic graph has diameterD, the time to decide ismin{O(nD/∆),n−Ω(n∆/D)}, even if D is not known in advance. Finally, we show that (a) there is a dynamic graph such that for every input, no node can decide before timen−O( ∆ 0.28 n 0.72); and (b) for any diameterD=O(∆), there is an execution with diameter D where no node can decide before time Ω(nD/∆). To our knowledge, our work constitutes the first study of ∆-coordinated consensus in general graphs.

Abstract. The topic of this paper is the study of Information Dissemination in Mobile Ad-hoc Networks by means of deterministic protocols. We characterize the connectivity resulting from the movement, from failures and from the fact that nodes may join the computation at different times with two values, α and β, so that, within α time slots, some node that has the information must be connected to some node without it for at least β time slots. The protocols studied are classified into three classes: oblivious (the transmission schedule of a node is only a function of its ID), quasi-oblivious (the transmission schedule may also depend on a global time), and adaptive. The main contribution of this work concerns negative results. Contrasting the lower and upper bounds derived, interesting complexity gaps among protocolclasses are observed. More precisely, in order to guarantee any progress towards solving the problem, it is shown that β must be at least n − 1 in general, but that β ∈ Ω(n 2 / log n) if an oblivious protocol is used. Since quasi-oblivious protocols can guarantee progress with β ∈ O(n), this represents a significant gap,

We consider a distributed task allocation problem in which m players must divide a set of n tasks between them. Each player i receives as input a set Xi of tasks such that the union of all input sets covers the task set. The goal is for each player to output a subset Yi ⊆ Xi, such that the outputs (Y1,..., Ym) form a partition of the set of tasks. The problem can be viewed as a distributed one-shot variant of the wellknown k-server problem, and we also show that it is closely related to the problem of finding a rooted spanning tree in directed broadcast networks. We study the communication complexity and round complexity of the task allocation problem. We begin with the classical two-player communication model, and show that the randomized communication complexity of task allocation is Ω(n), even when the set of tasks is known to the players in advance. For the multi-player setting with m = O(n) we give two upper bounds in the shared-blackboard model of communication. We show that the problem can be solved in O(log n) rounds and O(n log n) total bits for arbitrary inputs; moreover, if for any set X of tasks, there are at least α|X | players that have at least one task from X in their inputs, then O((1/α + log m) log n) rounds suffice even if each player can only write O(log n) bits on the blackboard in each round. Finally, we extend our results to the case where the players communicate over an arbitrary directed communication graph instead of a shared blackboard. As an application of these results, we also consider the related problem of constructing a directed spanning tree in stronglyconnected directed networks and we show lower and upper bounds for that problem.

Delay-tolerant networks (DTNs) are characterized by a possible absence of end-to-end communication routes at any instant. In most cases, however, a form of connectivity can be established over time and space. This particularity leads to consider the relevance of a given route not only in terms of hops (topological length), but also in terms of time (temporal length). The problem of measuring temporal distances between individuals in a social network was recently addressed, based on a posteriori analysis of interaction traces. This paper focuses on the distributed version of this problem, asking whether every node in a network can know precisely and in real time how out-ofdate it is with respect to every other. Answering affirmatively is simple when contacts between the nodes are punctual, using the temporal adaptation of vector clocks provided in [23]. It becomes more difficult when contacts have a duration and can overlap in time with each other. We demonstrate that the problem remains solvable with arbitrarily long contacts and non-instantaneous (though invariant and known) propagation delays on edges. This is done constructively by extending the temporal adaptation of vector clocks to non-punctual causality. The second part of the paper discusses how the knowledge of temporal lags could be used as a building block to solve more concrete problems, such as the construction of foremost broadcast trees or network backbones in periodically-varying DTNs.

Research Mission: To develop distributed algorithms that improve wireless networks. Distributed algorithms improve systems. We have repeatedly seen these algorithms begin in the theory community before migrating to real systems where they enabled performance breakthroughs. The massive data-centers now driving the Internet, for example, owe much to early theoretical work on consensus. Wireless networking, however, perhaps alone among the major networking technologies, has not yet seen this convergence between distributed algorithms and real systems. Though many theoreticians study distributed algorithms in this setting, their work is largely ignored by practitioners. It is as if the two communities are speaking different languages. This is a problem: by keeping these two concerns separate, we are potentially missing out on novel wireless system designs that would enable more functionality and better performance. I want to solve this problem by tackling hard theory problems that help real networks perform better. Here are two reasons to believe I can fulfill my mission: First, my training. I received my PhD in a theory group and am currently a postdoctoral associate in a systems group. Put another way, I am a theoretician, but I also speak the language of the networking community and actively seek collaboration. The second reason is my research record. A major goal of my work is to solve hard theory problems that are relevant to real networks. As summarized in Section 1, my efforts have resulted in a large number of publications in

This column focuses on the rather recent topic of dynamic communication networks, which are modeled as evolving graphs. Admittedly, the idea that a network can be dynamic is hardly new — networking research has been considering network topology changes and churn for decades. But by and large, past research considered such changes to be exceptions, and focused on adapting to them and re-stabilizing. Only in recent years, we begin to see works that treat dynamic changes as the norm. Such work on constantlyevolving networks may prove important in capturing many real world scenarios, in particular, ones that arise in wireless networks with mobile devices. In today’s column, Fabian Kuhn and Rotem Oshman survey recent work on dynamic networks. They consider adversarial as well as random models of graph evolution. In this context, they explain how the classical graph notions of diameter and cover time generalize to dynamic ones. These notions have important implications on information dissemination in the network. Fabian and Rotem then present an example algorithm for counting and information dissemination on adversarially evolving graphs. As research on dynamic networks is still in its infancy, many questions remain open; the column concludes with a discussion of some promising directions for future research. Many thanks to Fabian and Rotem for this survey! Call for contributions: I welcome suggestions for material to include in this column, including news, reviews, open problems, tutorials and surveys, either exposing the community to new and interesting topics, or providing new insight on well-studied topics by organizing them in new ways.

Efficient communication in wireless networks is typically challenged by the possibility of interference among several transmitting nodes. Much important research has been invested in decreasing the number of collisions in order to obtain faster algorithms for communication in such networks. This paper proposes a novel approach for wireless communication, which embraces collisions rather than avoiding them, over an additive channel. It introduces a coding technique called Bounded-Contention Coding (BCC) that allows collisions to be successfully decoded by the receiving nodes into the original transmissions and whose complexity depends on a bound on the contention among the transmitters. BCC enables deterministic local broadcast in a network with n nodes and at most a transmitters with information of ℓ bits each within O(a log n + aℓ) bits of communication with full-duplex radios, and O((a log n + aℓ)(log n)) bits, with high probability, with half-duplex radios. When combined with random linear network coding, BCC gives global broadcast within O((D + a + log n)(a log n + ℓ)) bits, with high probability. This also holds in dynamic networks that can change arbitrarily over time by a worst-case adversary. When no bound on the contention is given, it is shown how to probabilistically estimate it and obtain global broadcast that is adaptive to the true contention in the network. 1