Geographic Gossip: Efficient Averaging for Sensor Networks

Gossip algorithms for distributed computation are attractive due to their simplicity, distributed nature, and robustness in noisy and uncertain environments. However, using standard gossip algorithms can lead to a significant waste in energy by repeatedly recirculating redundant information. For realistic sensor network model topologies like grids and random geometric graphs, the inefficiency of gossip schemes is related to the slow mixing times of random walks on the communication graph. We propose and analyze an alternative gossiping scheme that exploits geographic information. By utilizing geographic routing combined with a simple resampling method, we demonstrate substantial gains over previously proposed gossip protocols. For regular graphs such as the ring or grid, our algorithm improves standard gossip by factors of $n$ and $\sqrt{n}$ respectively. For the more challenging case of random geometric graphs, our algorithm computes the true average to accuracy $\epsilon$ using $O(\frac{n^{1.5}}{\sqrt{\log n}} \log \epsilon^{-1})$ radio transmissions, which yields a $\sqrt{\frac{n}{\log n}}$ factor improvement over standard gossip algorithms. We illustrate these theoretical results with experimental comparisons between our algorithm and standard methods as applied to various classes of random fields.Comment: To appear, IEEE Transactions on Signal Processin

Greedy Gossip with Eavesdropping

This paper presents greedy gossip with eavesdropping (GGE), a novel randomized gossip algorithm for distributed computation of the average consensus problem. In gossip algorithms, nodes in the network randomly communicate with their neighbors and exchange information iteratively. The algorithms are simple and decentralized, making them attractive for wireless network applications. In general, gossip algorithms are robust to unreliable wireless conditions and time varying network topologies. In this paper we introduce GGE and demonstrate that greedy updates lead to rapid convergence. We do not require nodes to have any location information. Instead, greedy updates are made possible by exploiting the broadcast nature of wireless communications. During the operation of GGE, when a node decides to gossip, instead of choosing one of its neighbors at random, it makes a greedy selection, choosing the node which has the value most different from its own. In order to make this selection, nodes need to know their neighbors' values. Therefore, we assume that all transmissions are wireless broadcasts and nodes keep track of their neighbors' values by eavesdropping on their communications. We show that the convergence of GGE is guaranteed for connected network topologies. We also study the rates of convergence and illustrate, through theoretical bounds and numerical simulations, that GGE consistently outperforms randomized gossip and performs comparably to geographic gossip on moderate-sized random geometric graph topologies.Comment: 25 pages, 7 figure

An Efficient Data Aggregation Algorithm for Cluster-based Sensor Network

Data aggregation in wireless sensor networks eliminates redundancy to improve bandwidth utilization and energy-efficiency of sensor nodes. One node, called the cluster leader, collects data from surrounding nodes and then sends the summarized information to upstream nodes. In this paper, we propose an algorithm to select a cluster leader that will perform data aggregation in a partially connected sensor network. The algorithm reduces the traffic flow inside the network by adaptively selecting the shortest route for packet routing to the cluster leader. We also describe a simulation framework for functional analysis of WSN applications taking our proposed algorithm as an exampl

On the design and implementation of broadcast and global combine operations using the postal model

There are a number of models that were proposed in recent years for message passing parallel systems. Examples are the postal model and its generalization the LogP model. In the postal model a parameter λ is used to model the communication latency of the message-passing system. Each node during each round can send a fixed-size message and, simultaneously, receive a message of the same size. Furthermore, a message sent out during round r will incur a latency of hand will arrive at the receiving node at round r + λ - 1. Our goal in this paper is to bridge the gap between the theoretical modeling and the practical implementation. In particular, we investigate a number of practical issues related to the design and implementation of two collective communication operations, namely, the broadcast operation and the global combine operation. Those practical issues include, for example, 1) techniques for measurement of the value of λ on a given machine, 2) creating efficient broadcast algorithms that get the latency hand the number of nodes n as parameters and 3) creating efficient global combine algorithms for parallel machines with λ which is not an integer. We propose solutions that address those practical issues and present results of an experimental study of the new algorithms on the Intel Delta machine. Our main conclusion is that the postal model can help in performance prediction and tuning, for example, a properly tuned broadcast improves the known implementation by more than 20%

Some combinational optimization problems on radio network communication and machine scheduling

The combinatorial optimization problems coming from two areas are studied in this dissertation: network communication and machine scheduling. In the network communication area, the complexity of distributed broadcasting and distributed gossiping is studied in the setting of random networks. Two different models are considered: one is random geometric networks, the main model used to study properties of sensor and ad-hoc networks, where ri points are randomly placed in a unit square and two points are connected by an edge if they are at most a certain fixed distance r from each other. The other model is the so-called line-of-sight networks, a new network model introduced recently by Frieze et al. (SODA\u2707). The nodes in this model are randomly placed (with probability p) on an n x n grid and a node can communicate with all the nodes that are in at most a certain fixed distance r and which are in the same row or column. It can be shown that in many scenarios of both models, the random structure of these networks makes it possible to perform distributed gossiping in asymptotically optimal time 0(D), where D is the diameter of the network. The simulation results show that most algorithms especially the randomized algorithm works very fast in practice. In the scheduling area, the first problem is online scheduling a set of equal processing time tasks with precedence constraints so as to minimize the makespan. It can be shown that Hu \u27s algorithm yields an asymptotic competitive ratio of 3/2 for intree precedence constraints and an asymptotic competitive ratio of 1 for outtree precedences, and Coffinan-Graham algorithm yields an asymptotic competitive ratio of 1 for arbitrary precedence constraints and two machines.The second scheduling problem is the integrated production and delivery scheduling with disjoint windows. In this problem, each job is associated with a time window, and a profit. A job must be finished within its time window to get the profit. The objective is to pick a set ofjobs and schedule them to get the maximum total profit. For a single machine and unit profit, an optimal algorithm is proposed. For a single machine and arbitrary profit, a fully polynomial time approximation scheme(FPTAS) is proposed. These algorithms can be extended to multiple machines with approximation ratio less than e/(e - 1). The third scheduling problem studied in this dissertation is the preemptive scheduling algorithms with nested and inclusive processing set restrictions. The objective is to minimize the makespan of the schedule. It can be shown that there is no optimal online algorithm even for the case of inclusive processing set. Then a linear time optimal algorithm is given for the case of nested processing set, where all jobs are available for processing at time t = 0. A more complicated algorithm with running time 0(n log ri) is given that produces not only optimal but also maximal schedules. When jobs have different release times, an optimal algorithm is given for the nested case and a faster optimal algorithm is given for the inclusive processing set case

Compositional gossip: a conceptual architecture for designing gossip-based applications

Most proposed gossip-based systems use an ad-hoc design. We observe a low degree of reutilization among this proposals. We present how this limits both the systematic development of gossip-based applications and the number of applications that can benefit from gossip-based construction. We posit that these reinvent-the-wheel approaches poses a significant barrier to the spread and usability of gossip protocols. This paper advocates a conceptual design framework based upon aggregating basic and predefined building blocks BD 2. We show how to compose building blocks within our framework to construct more complex blocks to be used in gossip-based applications. The concept is further depicted with two gossip-based applications described using our building blocks.(undefined

Making Evildoers Pay: Resource-Competitive Broadcast in Sensor Networks

Consider a time-slotted, single-hop, wireless sensor network (WSN) consisting of n correct devices and and t=f*n Byzantine devices where f>=0 is any constant; that is, the Byzantine devices may outnumber the correct ones. There exists a trusted sender Alice who wishes to deliver a message m over a single channel to the correct devices. There also exists a malicious user Carol who controls the t Byzantine devices and uses them to disrupt the communication channel. For a constant k>=2, the correct and Byzantine devices each possess a meager energy budget of O(n^{1/k}), Alice and Carol each possess a limited budget of \tilde{O}(n^{1/k}), and sending or listening in a slot incurs unit cost. This general setup captures the inherent challenges of guaranteeing communication despite scarce resources and attacks on the network. Given this Alice versus Carol scenario, we ask: Is communication of m feasible and, if so, at what cost? We develop a protocol which, for an arbitrarily small constant \epsilon>0, ensures that at least (1-\epsilon)n correct devices receive m with high probability. Furthermore, if Carol's devices expend T energy jamming the channel, then Alice and the correct devices each spend only \tilde{O}(T^{1/(k+1)}). In other words, delaying the transmission of m forces a jammer to rapidly deplete its energy supply and, consequently, cease attacks on the network