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We present a system for efficient detection, continuous maintenance and visualization of range-constrained optimal density clusters of moving objects trajectories, a.k.a. Continuous Maximizing Range Sum (Co-MaxRS) queries. Co-MaxRS is useful in any domain involving continuous detection of “most interesting” regions involving mobile entities (e.g., traffic monitoring, environmental tracking, etc.). Traditional MaxRS finds a location of a given rectangle R which maximizes the sum of the weighted-points (objects) in its interior. Since moving objects continuously change their locations, the MaxRS at a particular time instant need not be a solution at another time instant. Our system solves two important problems: (1) Efficiently computing Co-MaxRS answer-set; and (2) Visualizing the results. This demo will present the implementation of our efficient pruning schemes and compact data structures, and illustrate the end-user tools for specifying the parameters and selecting datasets for Co-MaxRS, along with visualization of the optimal locations. 

We address the problem of maintaining the correct answer-sets to the Conditional Maximizing Range-Sum (C-MaxRS) query in spatial data streams. Given a set of (possibly weighted) 2D point objects, the traditional MaxRS problem determines an optimal placement for an axes-parallel rectangle r so that the number – or, the weighted sum – of objects in its interior is maximized. In many practical settings, the objects from a particular set – e.g., restaurants – can be of distinct types – e.g., fast-food, Asian, etc. The C-MaxRS problem deals with maximizing the overall sum, given class-based existential constraints, i.e., a lower bound on the count of objects of interests from particular classes. We first propose an efficient algorithm to the static C-MaxRS query, and extend the solution to handle dynamic (data streams) settings. Our experiments over datasets of up to 100,000 objects show that the proposed solutions provide significant efficiency benefits. 

We address the problem of efficient maintenance of the answer to a new type of query: Continuous Maximizing Range- Sum (Co-MaxRS) for moving objects trajectories. The traditional static/spatial MaxRS problem finds a location for placing the centroid of a given (axes-parallel) rectangle R so that the sum of the weights of the point-objects from a given set O inside the interior of R is maximized. However, moving objects continuously change their locations over time, so the MaxRS solution for a particular time instant need not be a solution at another time instant. In this paper, we devise the conditions under which a particular MaxRS solution may cease to be valid and a new optimal location for the query-rectangle R is needed. More specifically, we solve the problem of maintaining the trajectory of the centroid of R. In addition, we propose efficient pruning strategies (and corresponding data structures) to speed-up the process of maintaining the accuracy of the Co-MaxRS solution. We prove the correctness of our approach and present experimental evaluations over both real and synthetic datasets, demonstrating the benefits of the proposed methods. 

We address the problem of in-network processing of k-Maximizing Range Sum (k-MaxRS) queries inWireless Sensor Networks (WSN). The traditional, Computational Geometry version of the MaxRS problem considers the setting in which, given a set of (possibly weighted) 2D points, the goal is to determine the optimal location for a given (axes-parallel) rectangle R to be placed so that the sum of the weights (or, a simple count) of the input points in R’s interior is maximized. In WSN, this corresponds to finding the location of region R such that the sum of the sensors’ readings inside R is maximized. The k-MaxRS problem deals with maximizing the overall sum over k such rectangular regions. Since centralized processing – i.e., transmitting the raw readings and subsequently determining the k-MaxRS in a dedicated sink – incur communication overheads, we devised an efficient distributed algorithm for in-network computation of k-MaxRS. Our experimental observations show that the novel algorithm provides significant energy/communication savings when compared to the centralized approach.