K-nearest neighbors queries in time-dependent road networks: analyzing scenarios where points of interest move to the query point

Abstract

A kNN query retrieve the k points of interest that are closest to the query point, where proximity is computed from the query point to the points of interest. Time-dependent road networks are represented as weighted graphs, where the weight of an edge depends on the time one passes through that edge. This way, we can model periodic congestions during rush hour and similar effects. Travel time on road networks heavily depends on the traffic and, typically, the time a moving object takes to traverse a segment depends on departure time. In time-dependent networks, a kNN query, called TD-kNN, returns the k points of interest with minimum travel-time from the query point. As a more concrete example, consider the following scenario. Imagine a tourist in Paris who is interested to visit the touristic attraction closest from him/her. Let us consider two points of interest in the city, the Eiffel Tower and the Cathedral of Notre Dame. He/she asks a query asking for the touristic attraction whose the path leading up to it is the fastest at that time, the answer depends on the departure time. For example, at 10h it takes 10 minutes to go to the Cathedral. It is the nearest attraction. Although, if he/she asks the same query at 22h, in the same spatial point, the nearest attraction is the Eiffel Tower. In this work, we identify a variation of nearest neighbors queries in time-dependent road networks that has wide applications and requires novel algorithms for processing. Differently from TD-kNN queries, we aim at minimizing the travel time from points of interest to the query point. With this approach, a cab company can find the nearest taxi in time to a passenger requesting transportation. More specifically, we address the following query: find the k points of interest (e.g. taxi drivers) which can move to the query point (e.g. a taxi user) in the minimum amount of time. Previous works have proposed solutions to answer kNN queries considering the time dependency of the network but not computing the proximity from the points of interest to the query point. We propose and discuss a solution to this type of query which are based on the previously proposed incremental network expansion and use the A∗ search algorithm equipped with suitable heuristic functions. We also discuss the design and correctness of our algorithm and present experimental results that show the efficiency and effectiveness of our solution.