Performance Evaluation of Lazy Deletion Methods in R-trees

Motivated by the way R-trees are implemented in commercial databases systems, in this paper we examine several deletion techniques for R-trees. In particular, in commercial systems R-tree entries are mapped onto relational tables, which implement their own concurrency protocols on top of existing table-level concurrency mechanisms. In analogy, the actual industrial implementations of B-trees do not apply the well-known merging procedure from textbooks in case of node underflows, but rather they apply the free-at-empty technique. This way, space is sacrificed for the benefit of faster deletions and less locking operations, whereas the search performance practically remains unaffected.In this context, we examine the efficiency of modifications to the original R-tree deletion algorithm, which relax certain constraints of this algorithm and perform a controlled reorganization procedure according to a specified criterion. We present the modified algorithms and experimental results about the impact of these modifications on the tree quality, the execution time for the deletion operation and the processing time of search queries, considering several parameters. The experimental results indicate that the modified algorithms improve the efficiency of the deletion operation, while they do not affect the quality of the R-tree and its performance with respect to search operations