Statistical structures for internet-scale data management

Efficient query processing in traditional database management systems relies on statistics on base data. For centralized systems, there is a rich body of research results on such statistics, from simple aggregates to more elaborate synopses such as sketches and histograms. For Internet-scale distributed systems, on the other hand, statistics management still poses major challenges. With the work in this paper we aim to endow peer-to-peer data management over structured overlays with the power associated with such statistical information, with emphasis on meeting the scalability challenge. To this end, we first contribute efficient, accurate, and decentralized algorithms that can compute key aggregates such as Count, CountDistinct, Sum, and Average. We show how to construct several types of histograms, such as simple Equi-Width, Average-Shifted Equi-Width, and Equi-Depth histograms. We present a full-fledged open-source implementation of these tools for distributed statistical synopses, and report on a comprehensive experimental performance evaluation, evaluating our contributions in terms of efficiency, accuracy, and scalability

Estimating Answer Sizes for XML Queries

Abstract. Estimating the sizes of query results, and intermediate results, is crucial to many aspects of query processing. In particular, it is necessary for effective query optimization. Even at the user level, predictions of the total result size can be valuable in “next-step ” decisions, such as query refinement. This paper proposes a technique to obtain query result size estimates effectively in an XML database. Queries in XML frequently specify structural patterns, requiring specific relationships between selected elements. Whereas traditional techniques can estimate the number of nodes (XML elements) that will satisfy a node-specific predicate in the query pattern, such estimates cannot easily be combined to provide estimates for the entire query pattern, since element occurrences are expected to have high correlation. We propose a solution based on a novel histogram encoding of element occurrence position. With such position histograms, we are able to obtain estimates of sizes for complex pattern queries, as well as for simpler intermediate patterns that may be evaluated in alternative query plans, by means of a position histogram join (pH-join) algorithm that we introduce. We extend our technique to exploit schema information regarding allowable structure (the no-overlap property) through the use of a coverage histogram. We present an extensive experimental evaluation using several XML data sets, both real and synthetic, with a variety of queries. Our results demonstrate that accurate and robust estimates can be achieved, with limited space, and at a miniscule computational cost. These techniques have been implemented in the context of the TIMBER native XML database [22] at the University of Michigan.

Histograms and Wavelets on Probabilistic Data

There is a growing realization that uncertain information is a first-class citizen in modern database management. As such, we need techniques to correctly and efficiently process uncertain data in database systems. In particular, data reduction techniques that can produce concise, accurate synopses of large probabilistic relations are crucial. Similar to their deterministic relation counterparts, such compact probabilistic data synopses can form the foundation for human understanding and interactive data exploration, probabilistic query planning and optimization, and fast approximate query processing in probabilistic database systems. In this paper, we introduce definitions and algorithms for building histogram- and wavelet-based synopses on probabilistic data. The core problem is to choose a set of histogram bucket boundaries or wavelet coefficients to optimize the accuracy of the approximate representation of a collection of probabilistic tuples under a given error metric. For a variety of different error metrics, we devise efficient algorithms that construct optimal or near optimal B-term histogram and wavelet synopses. This requires careful analysis of the structure of the probability distributions, and novel extensions of known dynamic-programming-based techniques for the deterministic domain. Our experiments show that this approach clearly outperforms simple ideas, such as building summaries for samples drawn from the data distribution, while taking equal or less time

Processing count queries over event streams at multiple time granularities

Management and analysis of streaming data has become crucial with its applications in web, sensor data, network tra c data, and stock market. Data streams consist of mostly numeric data but what is more interesting is the events derived from the numerical data that need to be monitored. The events obtained from streaming data form event streams. Event streams have similar properties to data streams, i.e., they are seen only once in a fixed order as a continuous stream. Events appearing in the event stream have time stamps associated with them in a certain time granularity, such as second, minute, or hour. One type of frequently asked queries over event streams is count queries, i.e., the frequency of an event occurrence over time. Count queries can be answered over event streams easily, however, users may ask queries over di erent time granularities as well. For example, a broker may ask how many times a stock increased in the same time frame, where the time frames specified could be hour, day, or both. This is crucial especially in the case of event streams where only a window of an event stream is available at a certain time instead of the whole stream. In this paper, we propose a technique for predicting the frequencies of event occurrences in event streams at multiple time granularities. The proposed approximation method e ciently estimates the count of events with a high accuracy in an event stream at any time granularity by examining the distance distributions of event occurrences. The proposed method has been implemented and tested on di erent real data sets and the results obtained are presented to show its e ectiveness