Tunnel: Parallel-inducing sort for large string analytics

The suffix array is a crucial data structure for efficient string analysis. Over the course of twenty-six years, sequential suffix array construction algorithms have achieved O(n) time complexity and in-place sorting. In this paper, we present the Tunnel algorithm, the first large-scale parallel suffix array construction algorithm with a time complexity of O[Formula presented] based on the parallel random access machine (PRAM) model. The Tunnel algorithm is built on three key ideas: dividing the problem of size O(n) into p sub-problems of reduced size O[Formula presented] by replacing long suffixes with shorter prefixes of size at most a constant D; introducing a Tunnel mechanism to efficiently induce the order of a set of suffixes with long common prefixes; developing a strategy to transform a partially ordered suffix set into a total order relation by iteratively applying the Tunnel inducing method. We provide a detailed description of the algorithm, along with a thorough analysis of its time and space complexity, to demonstrate its correctness and efficiency. The proposed Tunnel algorithm exhibits scalable performance, making it suitable for large string analytics on large-scale parallel systems.