Optimal Gossip with Direct Addressing

Gossip algorithms spread information by having nodes repeatedly forward information to a few random contacts. By their very nature, gossip algorithms tend to be distributed and fault tolerant. If done right, they can also be fast and message-efficient. A common model for gossip communication is the random phone call model, in which in each synchronous round each node can PUSH or PULL information to or from a random other node. For example, Karp et al. [FOCS 2000] gave algorithms in this model that spread a message to all nodes in $\Theta(\log n)$ rounds while sending only $O(\log \log n)$ messages per node on average. Recently, Avin and Els\"asser [DISC 2013], studied the random phone call model with the natural and commonly used assumption of direct addressing. Direct addressing allows nodes to directly contact nodes whose ID (e.g., IP address) was learned before. They show that in this setting, one can "break the $\log n$ barrier" and achieve a gossip algorithm running in $O(\sqrt{\log n})$ rounds, albeit while using $O(\sqrt{\log n})$ messages per node. We study the same model and give a simple gossip algorithm which spreads a message in only $O(\log \log n)$ rounds. We also prove a matching $\Omega(\log \log n)$ lower bound which shows that this running time is best possible. In particular we show that any gossip algorithm takes with high probability at least $0.99 \log \log n$ rounds to terminate. Lastly, our algorithm can be tweaked to send only $O(1)$ messages per node on average with only $O(\log n)$ bits per message. Our algorithm therefore simultaneously achieves the optimal round-, message-, and bit-complexity for this setting. As all prior gossip algorithms, our algorithm is also robust against failures. In particular, if in the beginning an oblivious adversary fails any $F$ nodes our algorithm still, with high probability, informs all but $o(F)$ surviving nodes

Global Computation in a Poorly Connected World: Fast Rumor Spreading with No Dependence on Conductance

In this paper, we study the question of how efficiently a collection of interconnected nodes can perform a global computation in the widely studied GOSSIP model of communication. In this model, nodes do not know the global topology of the network, and they may only initiate contact with a single neighbor in each round. This model contrasts with the much less restrictive LOCAL model, where a node may simultaneously communicate with all of its neighbors in a single round. A basic question in this setting is how many rounds of communication are required for the information dissemination problem, in which each node has some piece of information and is required to collect all others. In this paper, we give an algorithm that solves the information dissemination problem in at most $O(D+\text{polylog}{(n)})$ rounds in a network of diameter $D$, withno dependence on the conductance. This is at most an additive polylogarithmic factor from the trivial lower bound of $D$, which applies even in the LOCAL model. In fact, we prove that something stronger is true: any algorithm that requires $T$ rounds in the LOCAL model can be simulated in $O(T +\mathrm{polylog}(n))$ rounds in the GOSSIP model. We thus prove that these two models of distributed computation are essentially equivalent

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

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 Nylon’s

GCP: Gossip-based Code Propagation for Large-scale Mobile Wireless Sensor Networks

Wireless sensor networks (WSN) have recently received an increasing interest. They are now expected to be deployed for long periods of time, thus requiring software updates. Updating the software code automatically on a huge number of sensors is a tremendous task, as ''by hand'' updates can obviously not be considered, especially when all participating sensors are embedded on mobile entities. In this paper, we investigate an approach to automatically update software in mobile sensor-based application when no localization mechanism is available. We leverage the peer-to-peer cooperation paradigm to achieve a good trade-off between reliability and scalability of code propagation. More specifically, we present the design and evaluation of GCP ({\emph Gossip-based Code Propagation}), a distributed software update algorithm for mobile wireless sensor networks. GCP relies on two different mechanisms (piggy-backing and forwarding control) to improve significantly the load balance without sacrificing on the propagation speed. We compare GCP against traditional dissemination approaches. Simulation results based on both synthetic and realistic workloads show that GCP achieves a good convergence speed while balancing the load evenly between sensors

LUNES: Agent-based Simulation of P2P Systems (Extended Version)

We present LUNES, an agent-based Large Unstructured NEtwork Simulator, which allows to simulate complex networks composed of a high number of nodes. LUNES is modular, since it splits the three phases of network topology creation, protocol simulation and performance evaluation. This permits to easily integrate external software tools into the main software architecture. The simulation of the interaction protocols among network nodes is performed via a simulation middleware that supports both the sequential and the parallel/distributed simulation approaches. In the latter case, a specific mechanism for the communication overhead-reduction is used; this guarantees high levels of performance and scalability. To demonstrate the efficiency of LUNES, we test the simulator with gossip protocols executed on top of networks (representing peer-to-peer overlays), generated with different topologies. Results demonstrate the effectiveness of the proposed approach.Comment: Proceedings of the International Workshop on Modeling and Simulation of Peer-to-Peer Architectures and Systems (MOSPAS 2011). As part of the 2011 International Conference on High Performance Computing and Simulation (HPCS 2011

Epidemic Information Diffusion: A Simple Solution to Support Community-based Recommendations in P2P Overlays

Epidemic protocols proved to be very efficient solutions for supporting dynamic and complex information diffusion in highly dis- tributed computing infrastructures, like P2P environments. They are useful bricks for building and maintaining virtual network topologies, in the form of overlay networks as well as to support pervasive diffusion of information when it is injected into the network. This paper proposes a simple architecture exploiting the features of epidemic approaches to foster a collaborative percolation of information between computing nodes belonging to the network aimed at building a system that groups similar users and spread useful information among them.Comment: 8 pages, 2 figure

Location-Aided Fast Distributed Consensus in Wireless Networks

Existing works on distributed consensus explore linear iterations based on reversible Markov chains, which contribute to the slow convergence of the algorithms. It has been observed that by overcoming the diffusive behavior of reversible chains, certain nonreversible chains lifted from reversible ones mix substantially faster than the original chains. In this paper, we investigate the idea of accelerating distributed consensus via lifting Markov chains, and propose a class of Location-Aided Distributed Averaging (LADA) algorithms for wireless networks, where nodes' coarse location information is used to construct nonreversible chains that facilitate distributed computing and cooperative processing. First, two general pseudo-algorithms are presented to illustrate the notion of distributed averaging through chain-lifting. These pseudo-algorithms are then respectively instantiated through one LADA algorithm on grid networks, and one on general wireless networks. For a $k\times k$ grid network, the proposed LADA algorithm achieves an $\epsilon$-averaging time of $O(k\log(\epsilon^{-1}))$. Based on this algorithm, in a wireless network with transmission range $r$, an $\epsilon$-averaging time of $O(r^{-1}\log(\epsilon^{-1}))$ can be attained through a centralized algorithm. Subsequently, we present a fully-distributed LADA algorithm for wireless networks, which utilizes only the direction information of neighbors to construct nonreversible chains. It is shown that this distributed LADA algorithm achieves the same scaling law in averaging time as the centralized scheme. Finally, we propose a cluster-based LADA (C-LADA) algorithm, which, requiring no central coordination, provides the additional benefit of reduced message complexity compared with the distributed LADA algorithm.Comment: 44 pages, 14 figures. Submitted to IEEE Transactions on Information Theor