Abstract
We address the problem of maintaining the correct answer-sets to a novel query—Conditional Maximizing Range-Sum (C-MaxRS)—for spatial data. Given a set of 2D point objects, possibly with associated weights, the traditional MaxRS problem determines an optimal placement for an axes-parallel rectangle r so that the number—or, the weighted sum—of the objects in its interior is maximized. The peculiarities of C-MaxRS is that in many practical settings, the objects from a particular set—e.g., restaurants—can be of different types—e.g., fast-food, Asian, etc. The C-MaxRS problem deals with maximizing the overall sum—however, it also incorporates class-based constraints, i.e., placement of r such that a lower bound on the count/weighted-sum of objects of interests from particular classes is ensured. We first propose an efficient algorithm to handle the static C-MaxRS query and then extend the solution to handle dynamic settings, where new data may be inserted or some of the existing data deleted. Subsequently we focus on the specific case of bulk-updates, which is common in many applications—i.e., multiple data points being simultaneously inserted or deleted. We show that dealing with events one by one is not efficient when processing bulk updates and present a novel technique to cater to such scenarios, by creating an index over the bursty data on-the-fly and processing the collection of events in an aggregate manner. Our experiments over datasets of up to 100,000 objects show that the proposed solutions provide significant efficiency benefits over the naïve approaches.
Highlights
Rapid advances in accuracy and miniaturization of location-aware devices, such as GPS-enabled smartphones, and increased use of social networks services have enabled a generation of large volumes of spatial data(e.g., Manyika et al, 2011)
To handle dynamic data stream scenarios, i.e., appearances and disappearances of objects, we propose two algorithms, Conditional Maximizing Range-Sum (C-Maximizing Range-Sum (MaxRS))+ and Conditional Maximizing Range-Sum (CMaxRS)−, respectively, which works as a backbone for solving the constrained maximum range sum queries in the dynamic insertions/deletions settings (C-MaxRS-DU)
A preliminary version of this paper has appeared in Mostafiz et al (2017), where we focused on non-weighted version of the C-MaxRS problem, i.e., we only count the number of objects inside the query window
Summary
Rapid advances in accuracy and miniaturization of location-aware devices, such as GPS-enabled smartphones, and increased use of social networks services (e.g., check-in updates) have enabled a generation of large volumes of spatial data(e.g., Manyika et al, 2011). The US Census Bureau has multiple surveys on geographic distributions of income categories and, for effective outreach purposes, the campaign managers would like to ensure that within the limited reachability from the headquarters, the staff has covered a maximum amount of voters—with the constraint that a minimum amount of representative from different categories are included This would correspond to the following query: Q1: “What should be the position of the headquarters at time t so that at least κi residents from each income Categoryi can be reached, while maximizing the number of voters reached, during that campaign date.”. Consider the following query: Q2: “What should be the position of an Internet-providing balloon at time t to ensure that there are at least i users from each Classi inside the balloon-coverage and the number of users in its coverage is maximized?”
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