Conditional MaxRS Query for Evolving Spatial Data

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.