Succinct Representations of Dynamic Strings

TL;DR

This paper introduces a space-efficient data structure for dynamically maintaining strings with fast rank, select, insert, and delete operations, improving on previous methods especially for small alphabets.

Contribution

The authors present a novel succinct dynamic string representation supporting efficient operations, optimized for small alphabets, with applications to space-efficient text indexing.

Findings

Supports rank, select, insert, delete in near-logarithmic time.

Achieves space usage close to the zero-order entropy of the string.

Improves the efficiency of space-efficient text index construction.

Abstract

The rank and select operations over a string of length n from an alphabet of size $\sigma$ have been used widely in the design of succinct data structures. In many applications, the string itself need be maintained dynamically, allowing characters of the string to be inserted and deleted. Under the word RAM model with word size $w=\Omega(\lg n)$, we design a succinct representation of dynamic strings using $nH_0 + o(n)\lg\sigma + O(w)$ bits to support rank, select, insert and delete in $O(\frac{\lg n}{\lg\lg n}(\frac{\lg \sigma}{\lg\lg n}+1))$ time. When the alphabet size is small, i.e. when $\sigma = O(\polylog (n))$, including the case in which the string is a bit vector, these operations are supported in $O(\frac{\lg n}{\lg\lg n})$ time. Our data structures are more efficient than previous results on the same problem, and we have applied them to improve results on the design and construction of space-efficient text indexes.