Applications to Other Variants of NN Queries

In this chapter, we show how CircularTrip or ArcTrip can be used to efficiently monitor the variants of NN queries. Our CircularTrip or ArcTrip based algorithms to answer such queries preserve the following properties

1. Algorithms visit minimum number of cells during the continuous monitoring of these queries

2. No extra book-keeping information is required to answer the queries

To the best of our knowledge, there is no existing approach that can efficiently monitor such queries. Though CPM can be used to answer such queries, it is easy to verify that CPM is not efficient.

The rest of the chapter is organized as follows. In section , we present algorithms for constrained NN queries. We present the technique to continuously monitor farthest neighbors in Section . ($k+m$ )-NN queries are discussed in Section .