Load-Balancing Succinct B Trees

TL;DR

This paper introduces space-efficient B tree representations that support fast operations and can be augmented with aggregate data, with applications to sparse suffix trees and LCP array computation.

Contribution

It presents novel succinct B tree data structures with optimized space and time complexities, including support for aggregate values and applications to suffix trees.

Findings

Supports all B tree operations in O(log n) or O(log n / log log n) time.

Uses space close to the information-theoretic lower bound.

Provides a linear-time algorithm for sparse LCP array computation.

Abstract

We propose a B tree representation storing $n$ keys, each of $k$ bits, in either (a) $nk + O(nk / \lg n)$ bits or (b) $nk + O(nk \lg \lg n/ \lg n)$ bits of space supporting all B tree operations in either (a) $O(\lg n )$ time or (b) $O(\lg n / \lg \lg n)$ time, respectively. We can augment each node with an aggregate value such as the minimum value within its subtree, and maintain these aggregate values within the same space and time complexities. Finally, we give the sparse suffix tree as an application, and present a linear-time algorithm computing the sparse longest common prefix array from the suffix AVL tree of Irving et al. [JDA'2003].