We consider the issues of implicitness and cache-obliviousness in the classical dictionary problem for n distinct keys over an unbounded and ordered universe. One finding in this paper is that of closing the longstanding open problem about the existence of an optimal implicit dictionary over an unbounded universe. Another finding is motivated by the antithetic features of implicit and cache-oblivious models in data structures. We show how to blend their best qualities achieving O(log n) time and O(logB n) block transfers for searching and for amortized updating, while using just n memory cells like sorted arrays and heaps. As a result, we avoid space wasting and provide fast data access at any level of the memory hierarchy.
['Gianni Franceschini', 'Roberto Grossi']
Optimal cache-oblivious implicit dictionaries