k-NN Search in Time-Dependent Road Networks

The ever-growing popularity of online map services and their wide deployment in smartphones and car-navigation systems have led to extensive use of location-based services. One of the most popular classes of such services is k-nearest neighbor (kNN) queries where users search for geographical points of interests (e.g., restaurants) and the corresponding directions and travel times to these locations in road networks. The online nature of these services requires almost instant response time. Accordingly, many algorithms have been developed to speed up kNN search in road networks by using a variety of precomputation techniques. However, all the existing approaches and commercial services for kNN search in road networks make the simplifying assumption that the fastest path between any two nodes in the network is unique by assuming the weight of each edge in the road network is constant. This assumption makes precomputation techniques feasible in terms of both preprocessing time and storage complexity. However, in the real world, the actual travel time on network edges depends on the arrival time to that edge – i.e., travel time is time dependent, and hence the fastest path between any nodes is not unique. It is infeasible to extend existing precomputation techniques to time-dependent road networks as input size (i.e., super-polynomial number of fastest paths) would increase drastically by yielding exponential precomputation time and prohibitively large storage requirements. This entry introduces the problem of kNN search in time-dependent spatial networks where the weight of each edge is a function of arrival time and studies an algorithm based on two novel indexing schemes – Tight Network Index (TNI ) and Loose Network Index (LNI ) – that enables efficient kNN search. The main idea of the algorithm is to localize the search and reduce the problem to a point location problem by decoupling the process of computing k-nearest neighbors from the invocation of expensive distance computation in network space.