Fast Approximate Reconciliation of Set Differences

We present new, simple, efficient data structures for approximate reconciliation of set differences, a useful standalone primitive for peer-to-peer networks and a natural subroutine in methods for exact reconciliation. In the approximate reconciliation problem, peers A and B respectively have subsets of elements SA and SB of a large universe U. Peer A wishes to send a short message M to peer B with the goal that B should use M to determine as many elements in the set SB–SA as possible. To avoid the expense of round trip communication times, we focus on the situation where a single message M is sent. We motivate the performance tradeoffs between message size, accuracy and computation time for this problem with a straightforward approach using Bloom filters. We then introduce approximation reconciliation trees, a more computationally efficient solution that combines techniques from Patricia tries, Merkle trees, and Bloom filters. We present an analysis of approximation reconciliation trees and provide experimental results comparing the various methods proposed for approximate reconciliation.

The Practice and Understanding of the Eucharist in the United Church of Christ: A Practical Theological Study

This dissertation explores the complexity of the understanding and practice of the Eucharist in the United Church of Christ as revealed in a textual analysis of the UCC Book of Worship (1986) and a qualitative study of five representative UCC congregations. Little has been written on this topic, save for several brief articles on the history of the theology of the sacrament in the two bodies that merged to form the UCC in 1957: the Congregational Christian Churches (CC) and the Evangelical and Reformed Church (E&R). This dissertation advances the topic through a practical-theological study that brings into critical conversation contemporary eucharistic practices in five congregations and a historical theological analysis of liturgical traditions in the UCC and antecedent denominations. Through this conversation, the study articulates common themes of a UCC eucharistic theology and explores implications for ongoing theology and practice in the denomination. The introduction explicates the methodology employed in this study, guided by Don Browning's work. The first two chapters present the findings of the focus group interviews and an interpretation of those results respectively. Chapter three analyzes the eucharistic liturgies in three historic books of worship used in the E&R heritage. In chapter four, two of the antecedent resources utilized in the CC tradition are analyzed. The short-lived Hymnal of the United Church of Christ, published in 1974, includes liturgies that would find fuller expression in the 1986 Book of Worship. That hymnal is examined in chapter five. Chapter six interprets the two services of "Word and Sacrament" found in the Book of Worship. Chapter seven offers a comparative analysis of the focus group findings and the theology inherent in the Book of Worship. The final chapter offers strategic recommendations for revised theory and practice. The conclusion points toward areas for further research: it propels a critical conversation around the notion of covenant, Christ's presence in the meal, and who can receive and officiate at the Eucharist. This dissertation concludes that the UCC lives within a balance of multiple, complementary theologies and challenges the denomination to make stronger connections between the meal and mission, reconciliation, and tradition.

Informed Content Delivery Across Adaptive Overlay Networks

Overlay networks have emerged as a powerful and highly flexible method for delivering content. We study how to optimize throughput of large, multipoint transfers across richly connected overlay networks, focusing on the question of what to put in each transmitted packet. We first make the case for transmitting encoded content in this scenario, arguing for the digital fountain approach which enables end-hosts to efficiently restitute the original content of size n from a subset of any n symbols from a large universe of encoded symbols. Such an approach affords reliability and a substantial degree of application-level flexibility, as it seamlessly tolerates packet loss, connection migration, and parallel transfers. However, since the sets of symbols acquired by peers are likely to overlap substantially, care must be taken to enable them to collaborate effectively. We provide 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 messaging 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.