Memory-efficient algorithms for spatial network queries

Abstract

Incrementally finding the k nearest neighbors (kNN) in a spatial network is an important problem in location-based services. One method (INE) simply applies Dijkstra's algorithm. Another method (IER) computes the k nearest neighbors using Euclidean distance followed by computing their corresponding network distances, and then incrementally finds the next nearest neighbors in order of increasing Euclidean distance until finding one whose Euclidean distance is greater than the current k nearest neighbor in terms of network distance. The LBC method improves on INE by avoiding the visit of nodes that cannot possibly lead to the k nearest neighbors by using a Euclidean heuristic estimator, and on IER by avoiding the repeated visits to nodes in the spatial network that appear on the shortest paths to different members of the k nearest neighbors by performing multiple instances of heuristic search using a Euclidean heuristic estimator on candidate objects around the query point. LBC's drawback is that the maintenance of multiple instances of heuristic search (called wavefronts) requires k priority queues and the queue operations required to maintain them incur a high in-memory processing cost. A method (SWH) is proposed that utilizes a novel heuristic function which considers objects surrounding the query point together as a single unit, instead of as one destination at a time as in LBC, thereby eliminating the need for multiple wavefronts and needs just one priority queue. These results in a significant reduction in the in-memory processing cost components while having the same reduced cost of the access to the spatial network as LBC. SWH is also extended to support the incremental distance semi-join (IDSJ) query, which is a multiple query point generalization of the kNN query. In addition, SWH is shown to support landmark-based heuristic functions, thereby enabling it to be applied to non-spatial networks/graphs such as social networks. Comparisons of experiments on SWH for kNN queries with INE, the best single-wavefront method, show that SWH is 2.5 times faster, and with LBC, the best existing heuristic search method, show that SWH is 3.5 times faster. For IDSJ queries, SWH-IDSJ is 5 times faster than INE-IDSJ, and 4 times faster than LBC-IDSJ.