compute an OPTICS clustering. Variants Priority R-tree R*-tree R+ tree RR* tree Hilbert R-tree X-tree Algorithm Data layout Data in R-trees is organized in pages that can have a variable number of entries (up to some pre-defined maximum, and usually above a minimum fill). Each entry within a non-leaf node stores two pieces of data: a way of identifying a child node, and the bounding box of all entries within this child node. Leaf nodes store the data required for each child, often a point or bounding box representing the child and an external identifier for the child. For point data, the leaf entries can be just the points themselves. For polygon data (that often requires the storage of large polygons) the common setup is to store only the MBR (minimum bounding rectangle) of the polygon along with a unique identifier in the tree. Search In range searching, the input is a search rectangle (Query box). Searching is quite similar to searching in a B+ tree. The search starts from the root node of the tree. Every internal node contains a set of rectangles and pointers to the corresponding child node and every leaf node contains the rectangles of spatial objects (the pointer to some spatial object can be there). For every rectangle in a node, it has to be decided if it overlaps the search rectangle or not. If yes, the corresponding child node has to be searched also. Searching is done like this in a recursive manner until all overlapping nodes have been traversed. When a leaf node is reached, the contained bounding boxes (rectangles) are tested against the search rectangle and their objects (if there are any) are put into the result set if they lie within the search rectangle. For priority search such as nearest neighbor search, the query consists of a point or rectangle. The root node is inserted into the priority queue. Until the queue is empty or the desired number of results have been returned the search continues by processing the nearest entry in the queue. Tree nodes are expanded and their children reinserted. Leaf entries are returned when encountered in the queue. This approach can be used with various distance metrics, including great-circle distance for geographic data. Insertion To insert an object, the tree is traversed recursively from the root node. At each step, all rectangles in the current directory node are