Given a set D = {d 1 , d 2 , ..., d D } of D strings of total length n, our task is to report the "most relevant" strings for a given query pattern P . This involves somewhat more advanced query functionality than the usual pattern matching, as some notion of "most relevant" is involved. In information retrieval literature, this task is best achieved by using inverted indexes. However, inverted indexes work only for some predefined set of patterns. In the pattern matching community, the most popular pattern-matching data structures are suffix trees and suffix arrays. However, a typical suffix tree search involves going through all the occurrences of the pattern over the entire string collection, which might be a lot more than the required relevant documents.The first formal framework to study such kind of retrieval problems was given by Muthukrishnan [25]. He considered two metrics for relevance: frequency and proximity. He took a thresholdbased approach on these metrics and gave data structures taking O(n log n) words of space. We study this problem in a slightly different framework of reporting the top k most relevant documents (in sorted order) under similar and more general relevance metrics. Our framework gives linear space data structure with optimal query times for arbitrary score functions. As a corollary, it improves the space utilization for the problems in [25] while maintaining optimal query performance. We also develop compressed variants of these data structures for several specific relevance metrics.Here, |CSA| denotes space (in bits) of the compressed suffix array (CSA) [17] of the given documents in D. It is shown that the average bits per character, |CSA|/n, is close to the empirical entropy of the documents. † Space is optimal in the non-succinct manner.

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Ranking is an important property that needs to be fully supported by current relational query engines. Recently, several rank-join query operators have been proposed based on rank aggregation algorithms. Rank-join operators progressively rank the join results while performing the join operation. The new operators have a direct impact on traditional query processing and optimization.We introduce a rank-aware query optimization framework that fully integrates rank-join operators into relational query engines. The framework is based on extending the System R dynamic programming algorithm in both enumeration and pruning. We define ranking as an interesting property that triggers the generation of rank-aware query plans. Unlike traditional join operators, optimizing for rank-join operators depends on estimating the input cardinality of these operators. We introduce a probabilistic model for estimating the input cardinality, and hence the cost of a rank-join operator. To our knowledge, this paper is the first effort in estimating the needed input size for optimal rank aggregation algorithms. Costing ranking plans, although challenging, is key to the full integration of rank-join operators in real-world query processing engines. We experimentally evaluate our framework by modifying the query optimizer of an open-source database management system. The experiments show the validity of our framework and the accuracy of the proposed estimation model.

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In many applications data values are inherently uncertain. This includes moving-objects, sensors and biological databases. There has been recent interest in the development of database management systems that can handle uncertain data. Some proposals for such systems include attribute values that are uncertain. In particular, an attribute value can be modeled as a range of possible values, associated with a probability density function. Previous efforts for this type of data have only addressed simple queries such as range and nearest-neighbor queries. Queries that join multiple relations have not been addressed in earlier work despite the significance of joins in databases. In this paper we address join queries over uncertain data. We propose a semantics for the join operation, define probabilistic operators over uncertain data, and propose join algorithms that provide efficient execution of probabilistic joins. The paper focuses on an important class of joins termed probabilistic threshold joins that avoid some of the semantic complexities of dealing with uncertain data. For this class of joins we develop three sets of optimization techniques: item-level, page-level, and index-level pruning. These techniques facilitate pruning with little space and time overhead, and are easily adapted to most join algorithms. We verify the performance of these techniques experimentally.

Abstract-The inherent uncertainty of data present in numerous applications such as sensor databases, text annotations, and information retrieval motivate the need to handle imprecise data at the database level. Uncertainty can be at the attribute or tuple level and is present in both continuous and discrete data domains. This paper presents a model for handling arbitrary probabilistic uncertain data (both discrete and continuous) natively at the database level. Our approach leads to a natural and efficient representation for probabilistic data. We develop a model that is consistent with possible worlds semantics and closed under basic relational operators. This is the first model that accurately and efficiently handles both continuous and discrete uncertainty. The model is implemented in a real database system (PostgreSQL) and the effectiveness and efficiency of our approach is validated experimentally.

Current data structures for searching large string collections either fail to achieve minimum space or cause too many cache misses. In this paper we discuss some edge linearizations of the classic trie data structure that are simultaneously cache-friendly and compressed. We provide new insights on front coding [24], introduce other novel linearizations, and study how close their space occupancy is to the information-theoretic minimum. The moral is that they are not just heuristics. Our second contribution is a novel dictionary encoding scheme that builds upon such linearizations and achieves nearly optimal space, offers competitive I/O-search time, and is also conscious of the query distribution. Finally, we combine those data structures with cacheoblivious tries [2, 5] and obtain a succinct variant whose space is close to the information-theoretic minimum.

We introduce a new variant of the popular Burrows-Wheeler transform (BWT) called Geometric Burrows-Wheeler Transform (GBWT). Unlike BWT, which merely permutes the text, GBWT converts the text into a set of points in 2-dimensional geometry. Using this transform, we can answer to many open questions in compressed text indexing: (1) Can compressed data structures be designed in external memory with similar performance as the uncompressed counterparts? (2) Can compressed data structures be designed for position restricted pattern matching [16]? We also introduce a reverse transform, called Points2Text, which converts a set of points into text. This transform allows us to derive the first known lower bounds in compressed text indexing. We show strong equivalence between data structural problems in geometric range searching and text pattern matching. This provides a way to derive new results in compressed text indexing by translating the results from range searching.