We use network coding to improve the speed of distributed computation in the dynamic network model of Kuhn, Lynch and Oshman [STOC '10]. In this model an adversary adaptively chooses a new network topology in every round, making even basic distributed computations challenging. show that n nodes, each starting with a d-bit token, can broadcast them to all nodes in time O(n^2) using b-bit messages, where b > d + log n. Their algorithms take the natural approach of token forwarding : in every round each node broadcasts some particular token it knows. They prove matching Omega(n^2) lower bounds for a natural class of token forwarding algorithms and an Omega(n log n) lower bound that applies to all token-forwarding algorithms. We use network coding, transmitting random linear combinations of tokens, to break both lower bounds. Our algorithm's performance is quadratic in the message size b, broadcasting the n tokens in roughly d b^2 * n^2 rounds. For b = d = O(log n) our algorithms use O(n^2 log n) rounds, breaking the first lower bound, while for larger message sizes we obtain linear-time algorithms. We also consider networks that change only every T rounds, and achieve an additional factor T^2 speedup. This contrasts with related lower and upper bounds of implying that for natural token-forwarding algorithms a speedup of T, but not more, can be obtained. Lastly, we give a general way to derandomize random linear network coding, that also leads to new deterministic information dissemination algorithms.
While traditional distributed algorithms research has focused on computation in static networks, the analysis of dynamic network topologies has gained importance both in practice and theory. @cite_7 offer an extensive review of this literature.
@cite_7
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The study of influential members of human networks is an important research question in social network analysis. However, the current state-of-the-art is based on static or aggregated representation of the network topology. We argue that dynamically evolving network topologies are inherent in many systems, including real online social and technological networks: fortunately the nature of these systems is such that they allow the gathering of large quantities of finegrained temporal data on interactions amongst the network members. In this paper we propose novel temporal centrality metrics which take into account such dynamic interactions over time. Using a real corporate email dataset we evaluate the important individuals selected by means of static and temporal analysis taking two perspectives: firstly, from a semantic level, we investigate their corporate role in the organisation; and secondly, from a dynamic process point of view, we measure information dissemination and the role of information mediators. We find that temporal analysis provides a better understanding of dynamic processes and a more accurate identification of important people compared to traditional static methods. The paper studies distributed static parameter (vector) estimation in sensor networks with nonlinear observation models and noisy intersensor communication. It introduces separably estimable observation models that generalize the observability condition in linear centralized estimation to nonlinear distributed estimation. It studies two distributed estimation algorithms in separably estimable models, the NU (with its linear counterpart LU) and the NLU. Their update rule combines a consensus step (where each sensor updates the state by weight averaging it with its neighbors' states) and an innovation step (where each sensor processes its local current observation). This makes the three algorithms of the consensus + innovations type, very different from traditional consensus. This paper proves consistency (all sensors reach consensus almost surely and converge to the true parameter value), efficiency, and asymptotic unbiasedness. For LU and NU, it proves asymptotic normality and provides convergence rate guarantees. The three algorithms are characterized by appropriately chosen decaying weight sequences. Algorithms LU and NU are analyzed in the framework of stochastic approximation theory; algorithm NLU exhibits mixed time-scale behavior and biased perturbations, and its analysis requires a different approach that is developed in this paper. The number of telecommunication networks deployed in a dynamic environment is quickly growing. This trend exists both in everyday life (e.g., smartphones, vehicles, and commercial satellites) and in a military context (e.g., dismounted soldiers or swarms of UAVs). Unfortunately, few theoretical tools to date have enabled the study of dynamic networks in a formal and rigorous way. As a result, it is hard and sometimes impossible to guarantee, mathematically, that a given algorithm will reach its objectives once deployed in real conditions. In this report, we identify a collection of recent theoretical tools whose purpose is to model, describe, and leverage dynamic networks in a formal way. These tools include a dynamic graph formalism, various computational models, and communication models for distributed networks. We extend many graph theoretical concepts towards a dynamic variant and show how these new variants impact the solution of classical distributed problems. The report also presents a hierarchy of dynamic networks based on dynamic graph properties, thereby offering a combinatorial alternative to the well-known mobility models typically used in simulations. Recent studies have observed that large data center networks often have a few hotspots while most of the network is underutilized. Consequently, numerous data center network designs have explored the approach of identifying these communication hotspots in real-time and eliminating them by leveraging flexible optical or wireless connections to dynamically alter the network topology. These proposals are based on the premise that statically wired network topologies, which lack the opportunity for such online optimization, are fundamentally inefficient, and must be built at uniform full capacity to handle unpredictably skewed traffic. We show this assumption to be false. Our results establish that state-of-the-art static networks can also achieve the performance benefits claimed by dynamic, reconfigurable designs of the same cost: for the skewed traffic workloads used to make the case for dynamic networks, the evaluated static networks can achieve performance matching full-bandwidth fat-trees at two-thirds of the cost. Surprisingly, this can be accomplished even without relying on any form of online optimization, including the optimization of routing configuration in response to the traffic demands. Our results substantially lower the barriers for improving upon today's data centers by showing that a static, cabling-friendly topology built using commodity equipment yields superior performance when combined with well-understood routing methods.