The log-structured merge-tree (LSM-tree)
Acta Informatica
On the analysis of indexing schemes
PODS '97 Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
A lower bound theorem for indexing schemes and its application to multidimensional range queries
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Tight bounds for 2-dimensional indexing schemes
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
On two-dimensional indexability and optimal range search indexing
PODS '99 Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Journal of the ACM (JACM)
On external memory graph traversal
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Optimal static range reporting in one dimension
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
On a model of indexability and its bounds for range queries
Journal of the ACM (JACM)
Optimal bounds for the predecessor problem and related problems
Journal of Computer and System Sciences - STOC 1999
Lower bounds for external memory dictionaries
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Incremental Organization for Data Recording and Warehousing
VLDB '97 Proceedings of the 23rd International Conference on Very Large Data Bases
A Novel Index Supporting High Volume Data Warehouse Insertion
VLDB '99 Proceedings of the 25th International Conference on Very Large Data Bases
On dynamic range reporting in one dimension
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Optimal External Memory Planar Point Enclosure
Algorithmica
Dynamic external hashing: the limit of buffering
Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures
On the cell probe complexity of dynamic membership
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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The B-tree is a fundamental external index structure that is widely used for answering one-dimensional range reporting queries. Given a set of N keys, a range query can be answered in O(logB NoverM + KoverB) I/Os, where B is the disk block size, K the output size, and M the size of the main memory buffer. When keys are inserted or deleted, the B-tree is updated in O(logB N) I/Os, if we require the resulting changes to be committed to disk right away. Otherwise, the memory buffer can be used to buffer the recent updates, and changes can be written to disk in batches, which significantly lowers the amortized update cost. A systematic way of batching up updates is to use the logarithmic method, combined with fractional cascading, resulting in a dynamic B-tree that supports insertions in O(1overB log NoverM) I/Os and queries in O(log NoverM + KoverB) I/Os. Such bounds have also been matched by several known dynamic B-tree variants in the database literature. Note that, however, the query cost of these dynamic B-trees is substantially worse than the O(logB NoverM + KoverB) bound of the static B-tree by a factor of ?(log B). In this paper, we prove that for any dynamic one dimensional range query index structure with query cost O(q + KoverB) and amortized insertion cost O(u/B), the tradeoff q · log(u/q) = ©(log B) must hold if q = O(log B). For most reasonable values of the parameters, we have NoverM = BO(1), in which case our query-insertion tradeoff implies that the bounds mentioned above are already optimal. We also prove a lower bound of u · log q = ©(log B), which is relevant for larger values of q. Our lower bounds hold in a dynamic version of the indexability model, which is of independent interests. Dynamic indexability is a clean yet powerful model for studying dynamic indexing problems, and can potentially lead to more interesting complexity results.