Sorabh Gandhi

eBay in the Sky: strategy-proof wireless spectrum auctions

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.

A General Framework for Wireless Spectrum Auctions

We propose a real-time spectrum auction framework to distribute spectrum among a large number wireless users under interference constraints. Our approach achieves conflict-free spectrum allocations that maximize auction revenue and spectrum utilization. Our design includes a compact and yet highly expressive bidding language, various pricing models to control tradeoffs between revenue and fairness, and fast auction clearing algorithms to compute revenue-maximizing prices and allocations. Both analytical and experimental results verify the efficiency of the proposed approach. We conclude that bidding behaviors and pricing models have significant impact on auction outcomes. A spectrum auction system must consider local demand and spectrum availability in order to maximize revenue and utilization.

Towards real-time dynamic spectrum auctions

In this paper, we propose a low-complexity auction framework to distribute spectrum in real-time among a large number of wireless users with dynamic traffic. Our design consists of a compact and highly expressive bidding format, two pricing models to control tradeoffs between revenue and fairness, and fast auction clearing algorithms to achieve conflict-free spectrum allocations that maximize auction revenue. We develop analytical bounds on algorithm performance and complexity to verify the efficiency of the proposed approach. We also use both simulated and real deployment traces to evaluate the auction framework. We conclude that pricing models and bidding behaviors have significant impact on auction outcomes and spectrum utilization. Any efficient spectrum auction system must consider demand and spectrum availability in local regions to maximize system-wide revenue and spectrum utilization.

Catching elephants with mice: Sparse sampling for monitoring 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/&epsis; log 1/&epsis;) sensor nodes (mice) is sufficient to catch any, and only those, events that affect Ω (&epsis;n) nodes (elephants), for any 0 < &epsis; < 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 ±&epsis;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.

GAMPS: compressing multi sensor data by grouping and amplitude scaling

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.

Contour approximation in sensor networks

We propose a distributed scheme called Adaptive-Group-Merge for sensor networks that, given a parameter k, approximates a geometric shape by a k-vertex polygon. The algorithm is well suited to the distributed computing architecture of sensor networks, and we prove that its approximation quality is within a constant factor of the optimal. We also show through simulation that our scheme outperforms several other alternatives in preserving important shape features, and achieves approximation quality almost as good as the optimal, centralized scheme. Because many applications of sensor networks involve observations and monitoring of physical phenomena, the ability to represent complex geometric shapes faithfully but using small memory is vital in many settings.

Approximate isocontours and spatial summaries for sensor networks

We consider the problem of approximating a family of isocontours in a sensor field 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 Theta(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 in- network aggregation and summarization of spatial data in sensor networks.

Space-efficient online approximation of time series data: Streams, amnesia, and out-of-order

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 L2 or 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.

Target Counting under Minimal Sensing: Complexity and Approximations

We consider the problem of counting a set of discrete point targets using a network of sensors under a minimalistic model. Each sensor outputs a single integer, the number of distinct targets in its range, but targets are otherwise indistinguishable to sensors: no angles, distances, coordinates, or other target-identifying measurements are available. This minimalistic model serves to explore the fundamental performance limits of low-cost sensors for such surveillance tasks as estimating the number of people, vehicles or ships in a field of interest to first degree of approximation, to be followed by more expensive sensing and localization if needed. This simple abstract setting allows us to explore the intrinsic complexity of a fundamental problem, and derive rigorous worst-case performance bounds. We show that even in the 1-dimensional setting (for instance, sensors counting vehicles on a road), the problem is non-trivial: target count can be estimated within relative accuracy of factor

Catching elephants with mice: sparse sampling for monitoring sensor networks

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