An implicit data structure for the dictionary problem maintains n data values in the first n locations of an array in such a way that it efficiently supports the operations insert, delete and search. No information other than that in O(1) memory cells and in the input data is to be retained; and the only operations performed on the data values (other than reads and writes) are comparisons. This paper describes the implicit B-tree, a new data structure supporting these operations in O(logBn) block transfers like in regular B-trees, under the realistic assumption that a block stores B = Ω(log n) keys, so that reporting r consecutive keys in sorted order has a cost of O(logBn+r/B) block transfers. En route a number of space efficient techniques for handling segments of a large array in a memory hierarchy are developed. Being implicit, the proposed data structure occupies exactly ⌈n/B⌉ blocks of memory after each update, where n is the number of keys after each update and B is the number of keys contained in a memory block. In main memory, the time complexity of the operations is O(log2n/loglog n), disproving a conjecture of the mid 1980s. © 2003 Elsevier Inc. All rights reserved.
Franceschini, G., Grossi, R., Munro, J. I., & Pagli, L. (2004). Implicit B-trees: A new data structure for the dictionary problem. In Journal of Computer and System Sciences (Vol. 68, pp. 788–807). Academic Press Inc. https://doi.org/10.1016/j.jcss.2003.11.003