Indexing Metric Uncertain Data for Range Queries

Abstract

Range queries in metric spaces have applications in many areas such as multimedia retrieval, computational biology, and locationbased services, where metric uncertain data exists in different forms, resulting from equipment limitations, high-throughput sequencing technologies, privacy preservation, or others. In this paper, we represent metric uncertain data by using an object-level model and a bi-level model, respectively. Two novel indexes, the uncertain pivot B + -tree (UPB-tree) and the uncertain pivot B + -forest (UPB-forest), are proposed accordingly in order to support probabilistic range queries w.r.t. a wide range of uncertain data types and similarity metrics. Both index structures use a small set of effective pivots chosen based on a newly defined criterion, and employ the B + -tree(s) as the underlying index. By design, they are easy to be integrated into any existing DBMS. In addition, we present efficient metric probabilistic range query algorithms, which utilize the validation and pruning techniques based on our derived probability lower and upper bounds. Extensive experiments with both real and synthetic data sets demonstrate that, compared against existing state-of-the-art indexes for metric uncertain data, the UPB-tree and UPB-forest incur much lower construction costs, consume smaller storage spaces, and can support more efficient metric probabilistic range queries.

Answering why-not questions on metric probabilistic range queries

“…Apart from probabilistic range queries in vector spaces, two alternatives for metric probabilistic range queries are studied [3,11]. Angiulli and Fassetti [3] propose a pivot-based index called UP-Index to prune uncertain objects using lower bound distances.…”

“…Angiulli and Fassetti [3] propose a pivot-based index called UP-Index to prune uncertain objects using lower bound distances. Chen et al [11] present UPB-tree and UPB-forest to further improve query efficiency. In addition, some efforts focus on probabilistic similarity queries on specific metric uncertain data, e.g., uncertain sets [17,30], uncertain strings [15,25], and uncertain graphs [26,33].…”

“…MMA pops the head entry q from H, and the while-loop cannot terminate as λ q × q < penalty. Next, MMA sets R′ to R (= 2), and performs an inner while-loop to increase R′ until the condition of Lemma 4 is satisfied (lines [11][12][13][14][15]. In the first iteration of the inner loop, as illustrated in Fig.…”

“…Most studies of metric probabilistic range retrieval aim to improve query efficiency and resource usage [3,11]. In contrast, comparably little attention has been given to query usability.…”

“…For example, as shown in Fig. 2, computer u 1 can be represented using preferences u 11 and u 12 , where each preference denotes the performance and price scores of u 1 from a user. A user issues an MPRQ to find computers that match the user's preference q = 2, 3, and the query returns {u 1 , u 2 }.…”