Parallel Construction of Suffix Trees and the All-Nearest-Smaller-Values Problem

A Suffix tree is a fundamental and versatile string data structure that is frequently used in important application areas such as text processing, information retrieval, and computational biology. Sequentially, the construction of suffix trees takes linear time, and optimal parallel algorithms exist only for the PRAM model. Recent works mostly target low core-count shared-memory implementations but achieve suboptimal complexity, and prior distributed-memory parallel algorithms have quadratic worst-case complexity. Suffix trees can be constructed from suffix and longest common prefix (LCP) arrays by solving the All-Nearest-Smaller-Values(ANSV) problem. In this paper, we formulate a more generalized version of the ANSV problem, and present a distributed-memory parallel algorithm for solving it in O(n/p +p) time. Our algorithm minimizes the overall and per-node communication volume. Building on this, we present a parallel algorithm for constructing a distributed representation of suffix trees, yielding both superior theoretical complexity and better practical performance compared to previous distributed-memory algorithms. We demonstrate the construction of the suffix tree for the human genome given its suffix and LCP arrays in under 2 seconds on 1024 Intel Xeon cores.