8,771 research outputs found

    Cooperative Convex Optimization in Networked Systems: Augmented Lagrangian Algorithms with Directed Gossip Communication

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    We study distributed optimization in networked systems, where nodes cooperate to find the optimal quantity of common interest, x=x^\star. The objective function of the corresponding optimization problem is the sum of private (known only by a node,) convex, nodes' objectives and each node imposes a private convex constraint on the allowed values of x. We solve this problem for generic connected network topologies with asymmetric random link failures with a novel distributed, decentralized algorithm. We refer to this algorithm as AL-G (augmented Lagrangian gossiping,) and to its variants as AL-MG (augmented Lagrangian multi neighbor gossiping) and AL-BG (augmented Lagrangian broadcast gossiping.) The AL-G algorithm is based on the augmented Lagrangian dual function. Dual variables are updated by the standard method of multipliers, at a slow time scale. To update the primal variables, we propose a novel, Gauss-Seidel type, randomized algorithm, at a fast time scale. AL-G uses unidirectional gossip communication, only between immediate neighbors in the network and is resilient to random link failures. For networks with reliable communication (i.e., no failures,) the simplified, AL-BG (augmented Lagrangian broadcast gossiping) algorithm reduces communication, computation and data storage cost. We prove convergence for all proposed algorithms and demonstrate by simulations the effectiveness on two applications: l_1-regularized logistic regression for classification and cooperative spectrum sensing for cognitive radio networks.Comment: 28 pages, journal; revise

    Finite-time Convergent Gossiping

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    Gossip algorithms are widely used in modern distributed systems, with applications ranging from sensor networks and peer-to-peer networks to mobile vehicle networks and social networks. A tremendous research effort has been devoted to analyzing and improving the asymptotic rate of convergence for gossip algorithms. In this work we study finite-time convergence of deterministic gossiping. We show that there exists a symmetric gossip algorithm that converges in finite time if and only if the number of network nodes is a power of two, while there always exists an asymmetric gossip algorithm with finite-time convergence, independent of the number of nodes. For n=2mn=2^m nodes, we prove that a fastest convergence can be reached in nm=nlogā”2nnm=n\log_2 n node updates via symmetric gossiping. On the other hand, under asymmetric gossip among n=2m+rn=2^m+r nodes with 0ā‰¤r<2m0\leq r<2^m, it takes at least mn+2rmn+2r node updates for achieving finite-time convergence. It is also shown that the existence of finite-time convergent gossiping often imposes strong structural requirements on the underlying interaction graph. Finally, we apply our results to gossip algorithms in quantum networks, where the goal is to control the state of a quantum system via pairwise interactions. We show that finite-time convergence is never possible for such systems.Comment: IEEE/ACM Transactions on Networking, In Pres

    Formal analysis techniques for gossiping protocols

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    We give a survey of formal verification techniques that can be used to corroborate existing experimental results for gossiping protocols in a rigorous manner. We present properties of interest for gossiping protocols and discuss how various formal evaluation techniques can be employed to predict them

    Gozar: NAT-friendly Peer Sampling with One-Hop Distributed NAT Traversal

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    Gossip-based peer sampling protocols have been widely used as a building block for many large-scale distributed applications. However, Network Address Translation gateways (NATs) cause most existing gossiping protocols to break down, as nodes cannot establish direct connections to nodes behind NATs (private nodes). In addition, most of the existing NAT traversal algorithms for establishing connectivity to private nodes rely on third party servers running at a well-known, public IP addresses. In this paper, we present Gozar, a gossip-based peer sampling service that: (i) provides uniform random samples in the presence of NATs, and (ii) enables direct connectivity to sampled nodes using a fully distributed NAT traversal service, where connection messages require only a single hop to connect to private nodes. We show in simulation that Gozar preserves the randomness properties of a gossip-based peer sampling service. We show the robustness of Gozar when a large fraction of nodes reside behind NATs and also in catastrophic failure scenarios. For example, if 80% of nodes are behind NATs, and 80% of the nodes fail, more than 92% of the remaining nodes stay connected. In addition, we compare Gozar with existing NAT-friendly gossip-based peer sampling services, Nylon and ARRG. We show that Gozar is the only system that supports one-hop NAT traversal, and its overhead is roughly half of Nylonā€™s

    Applying Formal Methods to Gossiping Networks with mCRL and Groove

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    In this paper we explore the practical possibilities of using formal methods to analyze gossiping networks. In particular, we use mCRL and Groove to model the peer sampling service, and analyze it through a series of model transformations to CTMCs and finally MRMs. Our tools compute the expected value of various network quality indicators, such as average path lengths, over all possible system runs. Both transient and steady state analysis are supported. We compare our results with the simulation and emulation results found in [10]
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