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Balanced graph partitioning in the streaming setting is a key problem to enable scalable and efficient computations on massive graph data such as web graphs, knowledge graphs, and graphs arising in the context of online social networks. Two families of heuristics for graph partitioning in the streaming setting are in wide use: place the newly arrived vertex… (More)

We define "random trip", a generic mobility model for independent mobiles that contains as special cases: the random waypoint on convex or non convex domains, random walk with reflection or wrapping, city section, space graph and other models. We use Palm calculus to study the model and give a necessary and sufficient condition for a stationary regime to… (More)

— We examine the fundamental properties that determine the basic performance metrics for op-portunistic communications. We first consider the distribution of inter-contact times between mobile devices. Using a diverse set of measured mobility traces, we find as an invariant property that there is a characteristic time, order of half a day, beyond which the… (More)

Motivated by the study of peer-to-peer file swarming systems à la BitTorrent, we introduce a probabilistic model of <i>coupon replication systems</i>. These systems consist of users, aiming to complete a collection of distinct coupons. Users are characterised by their current collection of coupons, and leave the system once they complete their coupon… (More)

The random trip model was recently proposed as a generic mobility model that contains many particular mobility models, including the widely-known random waypoint and random walks, and accommodates more realistic scenarios. The probability distribution of the movement of a mobile in all these models typically varies with time and converges to a "steady… (More)

We consider unicast equation-based rate control, where a source estimates the loss event ratio $p$, and, primarily at loss events, adjusts its send rate to $f(p)$. Function $f$ is assumed to represent the loss-throughput relation that TCP would experience. When no loss occurs, the rate may also be increased according to some additional mechanism. We assume… (More)

—Consider a network with an arbitrary topology and arbitrary communication delays, in which congestion control is based on additive–increase and multiplicative– decrease. We show that the source rates tend to be distributed in order to maximize an objective function called F h A (" F h A fairness "). We derive this result under the assumption of rate… (More)

— We consider a simple model of parallel TCP connections defined as follows. There are N connections competing for a bottleneck of fixed capacity. Each connection is assumed to increase its send rate linearly in time in absence of congestion indication and otherwise decreases its rate to a fraction β of the current send rate. Whenever aggregate send rate of… (More)

We consider the convergence time for solving the binary consensus problem using the interval consensus algorithm proposed by Bénézit, Thiran and Vetterli (2009). In the binary consensus problem, each node initially holds one of two states and the goal for each node is to correctly decide which one of these two states was initially held by a majority of… (More)

We consider epidemic-style information dissemination strategies that leverage the nonuniformity of host distribution over subnets (e.g., IP subnets) to optimize the information spread. Such epidemic-style strategies are based on random sampling of target hosts according to a sampling rule. In this paper, we consider the metric of total number of samplings… (More)