The efficient processing of nearest-neighbor queries in databases of moving objects is considered very important for applications such as fleet management, traffic control, digital battlefields and more. Such applications have been rapidly spread due to the fact that mobile computing and wireless technologies nowadays are ubiquitous. This chapter presents important aspects towards simple and incremental nearest-neighbor search for spatio-temporal databases. More specifically, we describe the algorithms that have already been proposed for simple and incremental nearest neighbor queries and present a new algorithm regarding that issue. Finally, we study the problem of keeping a query consistent in the presence of insertions, deletions and updates of moving objects.
