Abstract — Given a positive value r, a circular range query returns the objects that lie within the distance r of the query location. In this paper, we study the circular range queries that continuously change their locations. We present an efficient and effective technique to monitor such moving range queries by utilising the concept of a safe zone. The safe zone of a query is the area with a property that while the query remains inside it, the results of the query remain unchanged. Hence, the query does not need to be re-evaluated unless it leaves the safe zone. The shape of the safe zone is defined by the so-called guard objects. The cost of checking whether a query lies in the safe zone takes k distance computations, where k is the number of the guard objects. Our contributions are as follows. 1) We propose a technique based on powerful pruning rules and a unique access order which efficiently computes the safe zone and minimizes the I/O cost. 2) To show the effectiveness of the safe zone, we theoretically evaluate the probability that a query leaves the safe zone within one time unit and the expected distance a query moves before it leaves the safe zone. Additionally, for the queries that have diameter of the safe zone less than its expected value multiplied by a constant, we also give an upper bound on the expected number of guard objects. This upper bound turns out to be a constant, that is, it does not depend either on the radius r of the query or the density of the objects. The theoretical analysis is verified by extensive experiments. 3) Our thorough experimental study demonstrates that our proposed approach is close to optimal and is an order of magnitude faster than a naïve algorithm. I.

Abstract — Given a set of objects and a query q, apointp is called the reverse k nearest neighbor (RkNN) of q if q is one of the k closest objects of p. In this paper, we introduce the concept of influence zone which is the area such that every point inside this area is the RkNN of q and every point outside this area is not the RkNN. The influence zone has several applications in location based services, marketing and decision support systems. It can also be used to efficiently process RkNN queries. First, we present efficient algorithm to compute the influence zone. Then, based on the influence zone, we present efficient algorithms to process RkNN queries that significantly outperform existing best known techniques for both the snapshot and continuous RkNN queries. We also present a detailed theoretical analysis to analyse the area of the influence zone and IO costs of our RkNN processing algorithms. Our experiments demonstrate the accuracy of our theoretical analysis. I.

Given a set of objects and a query

In this paper, we study the problem of continuous monitoring of reverse

ABSTRACT Given a set of criterions, an object o dominates another object o ′ if o is more preferable than o ′ according to every criterion. A skyline query returns every object that is not dominated by any other object. In this paper, we study the problem of continuously monitoring a moving skyline query where one of the criterions is the distance between the objects and the moving query. We propose a safe zone based approach to address the challenge of efficiently updating the results as the query moves. A safe zone is the area such that the results of a query remain unchanged as long as the query lies inside this area. Hence, the results are required to be updated only when the query leaves its safe zone. Although the main focus of this paper is to present the techniques for Euclidean distance metric, the proposed techniques are applicable to any metric distance (e.g., Manhattan distance, road network distance). We present several non-trivial optimizations and propose an efficient algorithm for safe zone construction. Our experiments demonstrate that the cost of our safe zone based approach is reasonably close to a lower bound cost and is three orders of magnitude lower than the cost of a naïve algorithm.

In this paper, we propose a new location-aware pub/sub system, Elaps, that continuously monitors moving users subscribing to dy-namic event streams from social media and E-commerce applica-tions. Users are notified instantly when there is a matching event nearby. To the best of our knowledge, Elaps is the first to take into account continuous moving queries against dynamic event streams. Like existing works on continuous moving query processing, Elaps employs the concept of safe region to reduce communication over-head. However, unlike existing works which assume data from publishers are static, updates to safe regions may be triggered by newly arrived events. In Elaps, we develop a concept called impact region that allows us to identify whether a safe region is affected by newly arrived events. Moreover, we propose a novel cost model to optimize the safe region size to keep the communication overhead low. Based on the cost model, we design two incremental methods, iGM and idGM, for safe region construction. In addition, Elaps uses boolean expression, which is more expressive than keywords, to model user intent and we propose a novel index, BEQ-Tree, to handle spatial boolean expression matching. In our experiments, we use geo-tweets from Twitter and venues from Foursquare to simulate publishers and boolean expressions generated from AOL search log to represent users intentions. We test user movement in both synthetic trajectories and real taxi trajectories. The results show that Elaps can significantly reduce the communication over-head and disseminate events to users in real-time.

Given a positive value r, a distance based range query returns the objects that lie within the distance r of the query location. In this paper, we focus on the distance based range queries that continuously change their locations in a Euclidean space. We present an efficient and effective monitoring technique based on the concept of a safe zone. The safe zone of a query is the area with a property that while the query remains inside it, the results of the query remain unchanged. Hence, the query does not need to be re-evaluated unless it leaves the safe zone. Our contributions are as follows. 1) We propose a technique based on powerful pruning rules and a unique access order which efficiently computes the safe zone and minimizes the I/O cost. 2) We theoretically determine and experimentally verify the expected distance a query moves before leaving the safe zone and, for majority of queries, the expected number of guard objects. 3) Our experiments demonstrate that the proposed approach is close to optimal and is an order of magnitude faster than a naïve algorithm. 4) We also extend our technique to monitor the queries in a road network. Our algorithm is up to two order of magnitude faster than a naïve algorithm.

Spatial alarms are fundamental capability for location based advertisements and location based reminders. One of the most challenging problems in scaling spatial alarm processing is to compute alarm free regions (AFR) such that mobile objects traveling within an AFR can safely hibernate the alarm evaluation process until approaching the nearest alarm of interest. In this paper we argue that maintaining an index of both spatial alarms and empty regions (AFR in the context of spatial alarm processing) is critical for scalable processing of spatial alarms. Unfortunately, conventional spatial indexing methods, such as R-tree family, k-d tree, Quadtree, and Grid, are not well suited to index empty regions. We present Mondrian Tree − a region partitioning tree for indexing both spatial alarms and alarm free regions. We first introduce the Mondrian tree indexing algorithms, including index construction, search, and maintenance. Then we describe a suite of Mondrian tree optimizations to further enhance the performance of spatial alarm processing. Our experimental evaluation shows that the Mondrian tree index outperforms traditional index methods, such as R-tree, Grid, Quadtree, and k-d tree, for spatial alarm processing.

With ubiquitous wireless connectivity and technological advances in mobile devices, we witness the growing demands and increasing market shares of mobile intelligent systems and technologies for real-time decision making and location-based knowledge discovery. Spatial Alarms are considered as one of the fundamental capabilities for intelligent mobile location based systems. Like time based alarms that remind us the arrival of a future time point, spatial alarms remind us the arrival of a future spatial point. Existing approaches for scaling spatial alarm processing are focused on computing alarm free regions (AFR) and alarm free period (AFP) such that mobile objects traveling within an AFR can safely hibernate the alarm evaluation process for the computed AFP, to save battery power, until approaching the nearest alarm of interest. A key technical challenge in scaling spatial alarm processing is to efficiently compute AFR and AFP such that mobile objects traveling within an AFR can safely hibernate the alarm evaluation process during the computed AFP, while maintaining high accuracy. In this paper we argue that on-demand computation of AFR is expensive and may not scale well for dense population of mobile objects. Instead, we propose to maintain an index for both spatial alarms and empty regions (AFR) such that for a given mobile users location, we can find relevant spatial alarms and whether it is in an alarm free region more efficiently. We also show that conventional spatial indexing methods, such as R-tree family, k-d tree, Quadtree, and Grid, are by design not well suited to index empty regions. We present Mondrian Tree − a region partitioning tree for indexing both spatial alarms and alarm free regions. We first introduce the Mondrian Tree indexing algorithms, including index construction, search, and maintenance. Then we describe a suite of Mondrian Tree optimizations to further enhance the performance