Optimal Time Random Access to Grammar-Compressed Strings in Small Space

Abstract

The random access problem for compressed strings is to build a data structure that efficiently supports accessing the character in position $i$ of a string given in compressed form. Given a grammar of size $n$ compressing a string of size $N$, we present a data structure using $O(n\Delta {\log }_{\Delta }\frac{N}{n}\log N)$ bits of space that supports accessing position $i$ in $O({\log }_{\Delta }N)$ time for $\Delta \le {\log }^{O(1)}N$. The query time is optimal for polynomially compressible strings, i.e., when $n=O(N^{1-\epsilon })$.

Withdrawn because of errors in proofs. Fixed versions will be incorporated into a paper by other authors

References in corpus (2)

• Dynamic Integer Sets with Optimal Rank, Select, and Predecessor Search
• Rank, select and access in grammar-compressed strings