“…One categorization of the aforementioned structures is according to the family of the underlying access method used. In particular, there are approaches based either on R-trees or on Quadtrees as explained in (Raptopoulou, Vassilakopoulos, & Manolopoulos, 2004, 2006. On the other hand, these structures can be also partitioned into those that: (a) are based on geometric duality and represent the stored objects in the dual space (Agarwal, Arge, & Erickson, 2000;Kollios, Gunopulos, & Tsotras, 1999;Patel, Chen, & Chakka, 2004), and (b) leave the original representation intact by indexing data in their native dimensional space (Beckmann, Begel, Schneider, & Seeger, 1990;Papadopoulos, Kollios, Gunopulos, & Tsotras, 2002;Saltenis, Jensen, Leutenegger, & Lopez, 2000;Saltenis et al, 2001;Tao, Papadias, & Sun, 2003).…”