On the Recovery of R-Trees

Concurrent multidimensional index algorithms in page-server DBMS

“…There are two main approaches in dealing with R-tree structure modifications [14]. In the first approach, a strict R-tree consistency (i.e., minimum-bounding-rectangles are kept as tight as possible to improve R-tree search-time) is applied, while in the second approach, a relaxed R-tree consistency (minimum-bounding-rectangles are not kept as tight as possible) is applied.…”

“…In the strict R-tree consistency approach [14], when an updating transaction T (inserting or deleting an object) reaches a leaf node and finds out that a tree structure modification is needed, then T releases its S lock on that node and retraverses the R-tree from the root using lock-coupling with U locks, and U-locks all the pages on the tree structure modification path. Then T performs the structure modifications bottom-up on these pages, where the U locks on these pages are upgraded to X locks.…”

“…Then T performs the structure modifications bottom-up on these pages, where the U locks on these pages are upgraded to X locks. Each tree structure modification is logged using physiological redo-undo log records [10,12,14,15,16]. Hence, in the event of a system failure, all incomplete structure modifications must be undone first so that aborted transactions can be rolled back during the undo phase of the restart recovery.…”

“…In the relaxed R-tree consistency approach [14], a tree structure modification involving several levels of R-tree is divided into a sequence of small atomic actions. As in the first approach, when an updating transaction T reaches a leaf node and finds out that a tree structure modification is needed, then T releases its S lock on that node and retraverses the R-tree from the root using lock-coupling with U locks and executes structure modifications as atomic actions.…”

“…As in the first approach, when an updating transaction T reaches a leaf node and finds out that a tree structure modification is needed, then T releases its S lock on that node and retraverses the R-tree from the root using lock-coupling with U locks and executes structure modifications as atomic actions. Each structure modification upgrades the U locks to X-locks and updates three pages at a time on two adjacent levels in case of a page split (and one page on a single level of the R-tree in case of a minimum-bounding-rectangle modification), and is logged using a single physiological redo-only log record [12,14,15,16]. The X locks are released when the execution of an atomic structure modification is completed.…”