A tradeoff between search and update time for the implicit dictionary problem (Q1108806)

An implicit dictionary can be viewed as a set of allowable permutations together with an associated search algorithm and an associated update algorithm (a comparison-based model, with elements drawn from a totally ordered universe, is used in this paper). The authors study lower bounds for the search time, given a constant-time update algorithm. It is proved that if update is easy (constant-time), then situations in which search is difficult (super-logarithmic time) occur. The first and the final paragraphs constitute a very good exposition of related results, ideas and open problems.