In the emerging area of sensor-based systems, a significant challenge is to develop scalable, fault-tolerant methods to extract useful information from the data the sensors collect. An approach to this data management problem is the use of sensor database systems, which allow users to perform aggregation queries such as MIN, COUNT, and AVG on the readings of a sensor network. In addition, more advanced queries such as frequency counting and quantile estimation can be supported. Due to energy limitations in sensor-based networks, centralized data collection is generally impractical, so most systems use in-network aggregation to reduce network traffic. However, even these aggregation strategies remain bandwidth-intensive when combined with the fault-tolerant, multipath routing methods often used in these environments. To avoid this expense, we investigate the use of approximate in-network aggregation using small sketches. We present duplicate-insensitive sketching techniques that can be implemented efficiently on small sensor devices with limited hardware support and we analyze both their performance and accuracy. Finally, we present an experimental evaluation that validates the effectiveness of our methods.

In the emerging area of sensor-based systems, a significant challenge is to develop scalable, fault-tolerant methods to extract useful information from the data the sensors collect. An approach to this data management problem is the use of sensor database systems, exemplified by TinyDB and Cougar, which allow users to perform aggregation queries such as MIN, COUNT and AVG on a sensor network. Due to power and range constraints, centralized approaches are generally impractical, so most systems use in-network aggregation to reduce network traffic. However, these aggregation strategies become bandwidth-intensive when combined with the fault-tolerant, multipath routing methods often used in these environments. For example, duplicate-sensitive aggregates such as SUM cannot be computed exactly using substantially less bandwidth than explicit enumeration. To avoid this expense, we investigate the use of approximate in-network aggregation using small sketches. Our contributions are as follows: 1) we generalize well known duplicate-insensitive sketches for approximating COUNT to handle SUM, 2) we present and analyze methods for using sketches to produce accurate results with low communication and computation overhead, and 3) we present an extensive experimental validation of our methods.

Several spatio-temporal applications require the retrieval of summarized information about moving objects that lie in a query region during a query interval (e.g., the number of mobile users covered by a cell, traffic volume in a district, etc.). Existing solutions have the distinct counting problem: if an object remains in the query region for several timestamps during the query interval, it will be counted multiple times in the result. We solve this problem by integrating spatio-temporal indexes with sketches, traditionally used for approximate query processing. The proposed techniques can also be applied to reduce the space requirements of conventional spatio-temporal data and to mine spatio-temporal association rules.

A well-known paradigm for load balancing in parallel and distributed systems is the "power of two choices," whereby an item is stored at the less loaded of two (or more) random alternative servers. We investigate the power of two choices in natural settings where items and servers reside in a geometric space and each item is associated with the server that is its nearest neighbor. This is the setting for example in the Chord distributed hash table, where the geometric space is determined by clockwise distance on a one-dimensional ring. For example, our analysis shows that when $n$ items are placed at n servers with d choices per item, the maximum load at any server is log log n/ log d + O(1) with high probability, only an additive constant more than when servers are chosen uniformly at random. Our proofs are quite general, showing that the power of two choices works under a variety of distributions, with most geometric constructions having at most an additive O(1) penalty. We also show that these techniques still work under highly unbalanced distributions, and give sharp bounds on the necessary number of choices. Finally, we provide simulation results demonstrating the load balance that results as the system size scales into the millions.

Overlay networks have emerged as a powerful and highly flexible method for delivering content. We study how to optimize throughput of large transfers across richly connected, adaptive overlay networks, focusing on the potential of collaborative transfers between peers to supplement ongoing downloads. First, we make the case for an erasure-resilient encoding of the content. Using the digital fountain encoding approach, end hosts can efficiently reconstruct the original content of size n from a subset of any n symbols drawn from a large universe of encoding symbols. Such an approach affords reliability and a substantial degree of application-level flexibility, as it seamlessly accommodates connection migration and parallel transfers while providing resilience to packet loss. However, since the sets of encoding symbols acquired by peers during downloads may overlap substantially, care must be taken to enable them to collaborate effectively. Our main contribution is a collection of useful algorithmic tools for efficient summarization and approximate reconciliation of sets of symbols between pairs of collaborating peers, all of which keep message complexity and computation to a minimum. Through simulations and experiments on a prototype implementation, we demonstrate the performance benefits of our informed content-delivery mechanisms and how they complement existing overlay network architectures.

The first order isomorphism problem is to decide whether two nonrecursive types using product- and function-type constructors, are isomorphic under the axioms of commutative and associative products, and currying and distributivity of functions over products. We show that this problem can be solved in 2 is the input size. This result improves upon the space bounds of the best previous algorithm. We also describe an time algorithm for the linear isomorphism problem, which does not include the distributive axiom, whereby improving upon the time of the best previous algorithm for this problem.

Overlay networks have emerged as a powerful and highly flexible method for delivering content. We study how to optimize throughput of large transfers across richly connected, adaptive overlay networks, focusing on the potential of collaborative transfers between peers to supplement ongoing downloads. First, we make the case for an erasure-resilient encoding of the content. Using the digital fountain encoding approach, end-hosts can efficiently reconstruct the original content of size $n$ from a subset of any $n$ symbols drawn from a large universe of encoded symbols. Such an approach affords reliability and a substantial degree of application-level flexibility, as it seamlessly accommodates connection migration and parallel transfers while providing resilience to packet loss. However, since the sets of encoded symbols acquired by peers during downloads may overlap substantially, care must be taken to enable them to collaborate effectively. Our main contribution is a collection of useful algorithmic tools for efficient estimation, summarization, and approximate reconciliation of sets of symbols between pairs of collaborating peers, all of which keep message complexity and computation to a minimum. Through simulations and experiments on a prototype implementation, we demonstrate the performance benefits of our informed content delivery mechanisms and how they complement existing overlay network architectures.