I/O-Efficient Planar Range Skyline and Attrition Priority Queues

In the planar range skyline reporting problem, we store a set P of n 2D points in a structure such that, given a query rectangle Q = [a_1, a_2] x [b_1, b_2], the maxima (a.k.a. skyline) of P \cap Q can be reported efficiently. The query is 3-sided if an edge of Q is grounded, giving rise to two variants: top-open (b_2 = \infty) and left-open (a_1 = -\infty) queries. All our results are in external memory under the O(n/B) space budget, for both the static and dynamic settings: * For static P, we give structures that answer top-open queries in O(log_B n + k/B), O(loglog_B U + k/B), and O(1 + k/B) I/Os when the universe is R^2, a U x U grid, and a rank space grid [O(n)]^2, respectively (where k is the number of reported points). The query complexity is optimal in all cases. * We show that the left-open case is harder, such that any linear-size structure must incur \Omega((n/B)^e + k/B) I/Os for a query. We show that this case is as difficult as the general 4-sided queries, for which we give a static structure with the optimal query cost O((n/B)^e + k/B). * We give a dynamic structure that supports top-open queries in O(log_2B^e (n/B) + k/B^1-e) I/Os, and updates in O(log_2B^e (n/B)) I/Os, for any e satisfying 0 \le e \le 1. This leads to a dynamic structure for 4-sided queries with optimal query cost O((n/B)^e + k/B), and amortized update cost O(log (n/B)). As a contribution of independent interest, we propose an I/O-efficient version of the fundamental structure priority queue with attrition (PQA). Our PQA supports FindMin, DeleteMin, and InsertAndAttrite all in O(1) worst case I/Os, and O(1/B) amortized I/Os per operation. We also add the new CatenateAndAttrite operation that catenates two PQAs in O(1) worst case and O(1/B) amortized I/Os. This operation is a non-trivial extension to the classic PQA of Sundar, even in internal memory.Comment: Appeared at PODS 2013, New York, 19 pages, 10 figures. arXiv admin note: text overlap with arXiv:1208.4511, arXiv:1207.234

Continuous Spatial Query Processing:A Survey of Safe Region Based Techniques

In the past decade, positioning system-enabled devices such as smartphones have become most prevalent. This functionality brings the increasing popularity of location-based services in business as well as daily applications such as navigation, targeted advertising, and location-based social networking. Continuous spatial queries serve as a building block for location-based services. As an example, an Uber driver may want to be kept aware of the nearest customers or service stations. Continuous spatial queries require updates to the query result as the query or data objects are moving. This poses challenges to the query efficiency, which is crucial to the user experience of a service. A large number of approaches address this efficiency issue using the concept of safe region . A safe region is a region within which arbitrary movement of an object leaves the query result unchanged. Such a region helps reduce the frequency of query result update and hence improves query efficiency. As a result, safe region-based approaches have been popular for processing various types of continuous spatial queries. Safe regions have interesting theoretical properties and are worth in-depth analysis. We provide a comparative study of safe region-based approaches. We describe how safe regions are computed for different types of continuous spatial queries, showing how they improve query efficiency. We compare the different safe region-based approaches and discuss possible further improvements

Threshold interval indexing techniques for complicated uncertain data

Uncertain data is an increasingly prevalent topic in database research, given the advance of instruments which inherently generate uncertainty in their data. In particular, the problem of indexing uncertain data for range queries has received considerable attention. To efficiently process range queries, existing approaches mainly focus on reducing the number of disk I/Os. However, due to the inherent complexity of uncertain data, processing a range query may incur high computational cost in addition to the I/O cost. In this paper, I present a novel indexing strategy focusing on one-dimensional uncertain continuous data, called threshold interval indexing. Threshold interval indexing is able to balance I/O cost and computational cost to achieve an optimal overall query performance. A key ingredient of the proposed indexing structure is a dynamic interval tree. The dynamic interval tree is much more resistant to skew than R-trees, which are widely used in other indexing structures. This interval tree optimizes pruning by storing x-bounds, or pre-calculated probability boundaries, at each node. In addition to the basic threshold interval index, I present two variants, called the strong threshold interval index and the hyper threshold interval index, which leverage x-bounds not only for pruning but also for accepting results. Furthermore, I present a more efficient memory-loaded versions of these indexes, which reduce the storage size so the primary interval tree can be loaded into memory. Each index description includes methods for querying, parallelizing, updating, bulk loading, and externalizing. I perform an extensive set of experiments to demonstrate the effectiveness and efficiency of the proposed indexing strategies

RFID-Based Indoor Spatial Query Evaluation with Bayesian Filtering Techniques

People spend a significant amount of time in indoor spaces (e.g., office buildings, subway systems, etc.) in their daily lives. Therefore, it is important to develop efficient indoor spatial query algorithms for supporting various location-based applications. However, indoor spaces differ from outdoor spaces because users have to follow the indoor floor plan for their movements. In addition, positioning in indoor environments is mainly based on sensing devices (e.g., RFID readers) rather than GPS devices. Consequently, we cannot apply existing spatial query evaluation techniques devised for outdoor environments for this new challenge. Because Bayesian filtering techniques can be employed to estimate the state of a system that changes over time using a sequence of noisy measurements made on the system, in this research, we propose the Bayesian filtering-based location inference methods as the basis for evaluating indoor spatial queries with noisy RFID raw data. Furthermore, two novel models, indoor walking graph model and anchor point indexing model, are created for tracking object locations in indoor environments. Based on the inference method and tracking models, we develop innovative indoor range and k nearest neighbor (kNN) query algorithms. We validate our solution through use of both synthetic data and real-world data. Our experimental results show that the proposed algorithms can evaluate indoor spatial queries effectively and efficiently. We open-source the code, data, and floor plan at https://github.com/DataScienceLab18/IndoorToolKit