Bulk-Loading xBR $$^+$$ -trees

Bulk Insertions into xBR $$^{+}$$ -trees

“…In [11], an algorithm, called Process of Bulk Loading (PBL), for bulk-loading xBR + -trees for large datasets residing on disk was presented, using a limited amount of main memory.…”

“…• Up to the root level of m, we move to the parent of the node for which processing has been completed and we merge, one-by-one, the sub-trees that correspond to the siblings of this node with the xBR + -tree (Phase 4 of [11]). When merging of m with the xBR + -tree has been completed, the procedure returns to the previous stage of recursion, and if no changes in the structure of the index of the xBR + -tree have been done, the procedure will be continued with the next entry E and its corresponding subset B E .…”

“…-If none of these children has overflown, for each one of them, we update its DBR value and, if needed, we update DBR values of its ancestors (possibly, up to the root level) and the procedure returns to the previous stage of recursion. -If any child has overflown, we create an m-xBR + -tree (a main memory xBR + -tree) m for I (Phase 3 of [11]) and gradually merge m with the xBR + -tree, as follows.…”

“…• We merge, one-by-one, the sub-trees that correspond to the siblings of I m , from left to right, with the xBR + -tree (Phase 4 of [11]). At this stage, processing of I has been completed.…”

“…With this research work, we complete the design and implementation of methods to create and update an xBR + -tree from a dynamic dataset, since a new bulk-insertion method is proposed. That is, (1) in [11] a bulk-loading method is presented for xBR + -trees, (2) in [10] an efficient one-by-one-insertion procedure is defined and implemented for this new spatial index, and finally (3) in [13] a deletion algorithm is added to this index for removing object in a one-by-one fashion. There are two important aspects of the bulk-insertion methods.…”