In this paper, we present an abstract framework for online approximation of time-series data that yields a unified set of algorithms for several popular models: data streams, amnesic approximation, and out-of-order stream approximation. Our framework essentially develops a popular greedy method of bucket-merging into a more generic form, for which we can prove space-quality approximation bounds. When specialized to piecewise linear bucket approximations and commonly used error metrics, such as L2or L¿, our framework leads to provable error bounds where none were known before, offers new results, or yields simpler and unified algorithms. The conceptual simplicity of our scheme translates into highly practical implementations, as borne out in our simulation studies: the algorithms produce near-optimal approximations, require very small memory footprints, and run extremely fast.

We consider the problem of collectively approximating a set of sensor signals using the least amount of space so that any individual signal can be efficiently reconstructed within a given maximum (L∞) error ε. The problem arises naturally in applications that need to collect large amounts of data from multiple concurrent sources, such as sensors, servers and network routers, and archive them over a long period of time for offline data mining. We present GAMPS, a general framework that addresses this problem by combining several novel techniques. First, it dynamically groups multiple signals together so that signals within each group are correlated and can be maximally compressed jointly. Second, it appropriately scales the amplitudes of different signals within a group and compresses them within the maximum allowed reconstruction error bound. Our schemes are polynomial time O(α, β approximation schemes, meaning that the maximum (L∞) error is at most α ε and it uses at most β times the optimal memory. Finally, GAMPS maintains an index so that various queries can be issued directly on compressed data. Our experiments on several real-world sensor datasets show that GAMPS significantly reduces space without compromising the quality of search and query.

We propose a scalably efficient scheme for detecting large-scale physically correlated events in sensor networks. Specifically, we show that in a network of n sensors arbitrarily distributed in the plane, a sample of O (1/ϵ log 1/ϵ) sensor nodes ( mice ) is sufficient to catch any, and only those , events that affect Ω (ϵ n ) nodes ( elephants ), for any 0 < ϵ < 1, as long as the geometry of the event has a bounded Vapnik-Chervonenkis (VC) dimension. In fact, the scheme is provably able to estimate the size of an event within the approximation error of ±ϵ n /4, which can be improved further at the expense of more mice. The detection algorithm itself requires knowledge of the event geometry (e.g., circle, ellipse, or rectangle) for the sake of computational efficiency, but the combinatorial bound on the sample size (set of mice) depends only on the VC, dimension of the event class and not the precise shape geometry. While nearly optimal in theory, due to implicit constant factors, these “scale-free” bounds still prove too large in practice if applied blindly. We therefore propose heuristic improvements and perform empirical parameter tuning to counter the pessimism inherent in these theoretical estimates. Using a variety of data distributions and event geometries, we show through simulations that the final scheme is eminently scalable and practical, say, for n ≥ 1000. The overall simplicity and generality of our technique suggests that it is well suited for a wide class of sensornet applications, including monitoring of physical environments, network anomalies, network security, or any abstract binary event that affects a significant number of nodes in the network.

Market-driven dynamic spectrum auctions can drastically improve the spectrum availability for wireless networks struggling to obtain additional spectrum. However, they face significant challenges due to the fear of market manipulation. A truthful or strategy-proof spectrum auction eliminates the fear by enforcing players to bid their true valuations of the spectrum. Hence bidders can avoid the expensive overhead of strategizing over others and the auctioneer can maximize its revenue by assigning spectrum to bidders who value it the most. Conventional truthful designs, however, either fail or become computationally intractable when applied to spectrum auctions. In this paper, we propose VERITAS, a truthful and computationally-efficient spectrum auction to support an eBay-like dynamic spectrum market. VERITAS makes an important contribution of maintaining truthfulness while maximizing spectrum utilization. We show analytically that VERITAS is truthful, efficient, and has a polynomial complexity of O(n3k) when n bidders compete for k spectrum bands. Simulation results show that VERITAS outperforms the extensions of conventional truthful designs by up to 200% in spectrum utilization. Finally, VERITAS supports diverse bidding formats and enables the auctioneer to reconfigure allocations for multiple market objectives.

We consider the problem of approximating a family of isocontours in a sensor fleld with a topologically-equivalent family of simple polygons. Our algorithm is simple and distributed, it gracefully adapts to any user-specified representation size k, and it delivers a worst-case guarantee for the quality of approximation. In particular, we prove that the topology-respecting Hausdorff error in our k -vertex approximation is within a small constant factor of the optimal error possible with Θ(k/log m) vertices, where m is the number of contours. Evaluation of the algorithm on real data suggests that the size increase factor in practice is a constant near 2 .6, and shows no error increase. Our simulation results using a variety of synthetic and real data show that the algorithm smoothly handles complex isocontours, even for representation sizes as small as 32 or 48. Because isocontours are widely used to represent and communicate bi-variate signals, our technique is broadly applicable to innetwork aggregation and summarization of spatial data in sensor networks.

We propose a scalably efficient scheme for detecting large-scale physically-correlated events in sensor networks. Specifically, we show that in a network of n sensors arbitrarily distributed in the plane, a sample of O(1/ε log 1/ε) sensor nodes (mice) is sufficient to catch any, and only those, events that affect Ω(εn) nodes (elephants), for any 0 < ε < 1, as long as the geometry of the event has a bounded Vapnik-Chervonenkis (VC) dimension. In fact, the scheme is provably able to estimate the size of an event within the approximation error of ±εn/4, which can be improved further at the expense of more mice. The detection algorithm itself requires knowledge of the event geometry (e.g. circle, ellipse, or rectangle) for the sake of computational efficiency, but the combinatorial bound on the sample size (set of mice) depends only on the VC dimension of the event class and not the precise shape geometry.