Continuous nearest-neighbor search in the presence of obstacles

Abstract

Despite the ubiquity of physical obstacles (e.g., buildings, hills, and blindages, etc.) in the real world, most of spatial queries ignore the obstacles. In this article, we study a novel form of continuous nearest-neighbor queries in the presence of obstacles, namely continuous obstructed nearest-neighbor (CONN) search, which considers the impact of obstacles on the distance between objects. Given a data set P , an obstacle set O , and a query line segment q , in a two-dimensional space, a CONN query retrieves the nearest neighbor p ∈ P of each point p′ on q according to the obstructed distance, the shortest path between p and p ′ without crossing any obstacle in O . We formalize CONN search, analyze its unique properties, and develop algorithms for exact CONN query-processing assuming that both P and O are indexed by conventional data-partitioning indices (e.g., R-trees). Our methods tackle CONN retrieval by performing a single query for the entire query line segment, and only process the data points and obstacles relevant to the final query result via a novel concept of control points and an efficient quadratic-based split point computation approach. Then, we extend our techniques to handle variations of CONN queries, including (1) continuous obstructed k nearest neighbor (CO k NN) search which, based on obstructed distances, finds the k (≥ 1) nearest neighbors (NNs) to every point along q ; and (2) trajectory obstructed k nearest-neighbor (TO k NN) search, which, according to obstructed distances, returns the k NNs for each point on an arbitrary trajectory (consisting of several consecutive line segments). Finally, we explore approximate CO k NN (ACO k NN) retrieval. Extensive experiments with both real and synthetic datasets demonstrate the efficiency and effectiveness of our proposed algorithms under various experimental settings.