Mondrian tree: A fast index 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 article we argue that on-demand computation of Afr is expensive and may not scale well for dense populations of mobile objects. Instead, we propose to maintain an index for both spatial alarms and empty regions (Afr) such that for a given mobile user's 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 of spatial alarm processing. Our experimental evaluation shows that the Mondrian Tree index, as an intelligent technology for mobile systems, outperforms traditional index methods, such as R-tree, Quadtree, and k-d tree, for spatial alarm processing.