Parallel Construction of Succinct Trees

Abstract

Succinct representations of trees are an elegant solution to make large trees fit in main memory while still supporting navigational operations in constant time. However, their construction time remains a bottleneck. We introduce a practical parallel algorithm that improves the state of the art in succinct tree construction. Given a tree on $n$ nodes stored as a sequence of balanced parentheses, our algorithm builds a succinct tree representation in $O(n/p+\lg p)$ time, where $p$ is the number of available cores. The constructed representation uses $2n + o(n)$ bits of space and supports a rich set of operations in $O(\lg n)$ time. In experiments using up to 64 cores and on inputs of different sizes, our algorithm achieved good parallel speed-up. We also present an algorithm that takes $O(n/p + \lg p)$ time to construct the balanced parenthesis representation of the input tree required by our succinct tree construction algorithm.

This work was supported by the Emerging Leaders in the Americas scholarship programme, NSERC, and the Canada Research Chairs programme.