Optimal trade-offs for succinct string indexes

Abstract

Let s be a string whose symbols are solely available through access(i), a read-only operation that probes s and returns the symbol at position i in s. Many compressed data structures for strings, trees, and graphs, require two kinds of queries on s: select(c,j), returning the position in s containing the jth occurrence of c, and rank(c,p), counting how many occurrences of c are found in the first p positions of s. We give matching upper and lower bounds for this problem. The main contribution is to introduce a general technique for proving lower bounds on succinct data structures, that is based on the access patterns of the supported operations, abstracting from the particular operations at hand. © 2010 Springer-Verlag Berlin Heidelberg.