Discussion

The continuous monitoring of constrained nearest neighbor queries have become important. Recently, algorithms have been proposed to continuously monitor reverse nearest neighbor queries [XZ06,KMS$^+$07] and each algorithm needs to continuously monitor nearest neighbor in constrained regions. We have shown that our novel access methods CircularTrip and ArcTrip can be used to continuously monitor various continuous $k$ CNN queries. Our approach is flexible, efficient and can easily replace previous algorithms used for continuous monitoring of constrained nearest neighbor queries.

To show the flexibility of our approach we show that it can be extended to answer the continuous $k$ CNN queries where the constrained region can be changed at any time and for all the algorithms presented the number of visited cells is minimum. To the best of our knowledge there is no existing approach that can efficiently answer such queries. Though CPM can be used to compute the initial results of few of such queries by considering only the cells and rectangles that lie in the constrained region but the rectangle based partitioning of CPM is not specifically designed to prioritize cells based on their angle from $q$ so its performance becomes poor for continuous monitoring of such queries and even worse for varying constrained region CNN queries.