CircularTrip

In this section, we present and analyze our access method named CircularTrip. As described earlier, given a radius $r$ and a query location $q$ , CircularTrip returns a set of cells $C$ so that all the cells in it intersect the circle of radius $r$ with center at $q$ . Formally, $C_r = \{\forall c \vert  mindist(c,q)< r \leq maxdist(c,q)\}$ . Figure  shows an example where CircularTrip returns all the shaded cells. In Section , for the sake of simplicity we present CircularTrip for 2 dimensional grid structure then we will discuss its extension to higher dimensions in Section .