Discussion

To the best of our knowledge there is no efficient approach that can continuously monitor farthest neighbor queries. SEA-CNN and YPK-CNN are very inefficient because they are designed only to find the nearest neighbors of some query points. Extension of CPM to farthest neighbor queries is non-trivial. Moreover, a rectangle gives a better approximation only for smaller circles. As the size of circle grows, the approximation yielded by rectangle become worse. For this reason, CPM's approximation of proximity of cells to $q$ becomes worse once the rectangles becomes farther from query point which is the case for farthest neighbor queries. On the other hand, our grid access methods can easily monitor farthest neighbor queries without any performance degradation. This shows the effectiveness of our presented grid access methods.