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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.

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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 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.