A Cache-Oblivious Implicit Dictionary with the Working Set Property

Abstract

Abstract. In this paper we present an implicit dictionary with the working set property i.e. a dictionary supporting insert(e), delete(x) and predecessor(x) in O(log n) time and search(x) in O(log ) time, where n is the number of elements stored in the dictionary and is the number of distinct elements searched for since the element with key x was last searched for. The dictionary stores the elements in an array of size n using no additional space. In the cache-oblivious model the operations insert(e), delete(x) and predecessor(x) cause O(log B n) cache-misses and search(x) causes O(log B ) cache-misses.

Skyline Queries in O(1) time?

“…The MLR-tree consists of arrays L, R, P that could be trivially transformed in cache-oblivious model, a number o k recursive layers where the last layer (microtree) could be fit into cache (disk block) regardless of the cache size. Moreover, MLR-tree uses auxiliary data structures for predecessor and h-RMQ queries that have been already implemented in the cache-oblivious model (see [33] and [34] respectively). In addition, the improvement of update performance of MLR-tree constitutes a challenging open problem.…”

Finger Search in the Implicit Model

“…Elements in B i are closer to f than elements in B i+1 . The overflow structure O is an implicit movable dictionary [2] that supports move-left and move-right as described in the Section 1. See Figure 3 for the layout of the data structure.…”

“…In [5] an implicit B-tree is presented, and finally in [4] a worst case optimal and cache oblivious dictionary is presented. To prove our dynamic upper bounds we use the movable implicit dictionary presented in [2], supporting insert, delete, predecessor, successor, move-left and move-right. The operation move-right moves the dictionary laid out in cells i through j to i + 1 through j + 1 and move-left moves the dictionary the other direction.…”