Lower Bounds for Succinct Data Structures
Indexing text files with methods such as suffix trees and suffix arrays permits extremely fast search for substrings. Unfortunately the space cost of these can dominate that of the raw data. For example, the naive implementation of a suffix tree on genetic information could take 80 times as much space as the raw data. Succinct data structures offer a technique by which the extra space of the indexing can be kept, at least in principle, to a “little oh” with respect to the raw data. This begs the question of how much extra space is necessary to support fast substring searches of other queries such as the rank/select problem or representing a permutation so that both the forward permutation and its inverse can be determined quickly. We survey some lower bounds on this type of problem, most notably the work of Demaine and López-Ortiz and of Golynski.