A number of methods have been proposed for suffix sorting on internal memory of RAM and external memory of hard disks. The current best results for suffix sorting on internal or external memory are achieved by several algorithms using the induced sorting (IS) method in various ways. While these algorithms are efficient, the internal ones are much different from those external in terms of the algorithm designs. A scalable IS method that can be applied for suffix sorting on both internal and external memory is highly desired. This article proposes a blockwise IS method to facilitate pipelined access on internal memory and sequential I/Os on external memory. The detailed algorithm of using this method for a 4-stage pipeline with multiple threads is described, where multiple threads are applied to parallelize not only the pipelined stages of consecutive blocks but also the tasks within each stage wherever possible. This algorithm is evaluated by our experiments on a set of realistic and artificial datasets to achieve better overall time and space performance than the existing best results from pSACAK, pDSS and pKS. Beside sorting suffixes on internal memory in linear time, the proposed method can be ported to external memory for sorting massive suffixes in linear I/O complexity.

Jing Yi Xie, Renato Ferreira Pinto Junior, Graeme Hirst, Yang Xu. Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP). 2019.

Sorting all suffixes of an input string$X$will produce the suffix array that is a fundamental data structure for full-text search on$X$. To utilize the parallel computing power of a multicore machine with shared memory, this article designs a fast linear-time and in-place parallel algorithm called pSACAK, for sorting the suffixes of an input string with a constant alphabet. This algorithm is a parallel variant of the sequential suffix sorting algorithm SACAK which improved the linear-time SAIS to be in-place for constant alphabets, and hence requires only a workspace of$\mathcal {O}(K)$for alphabet size$K$. While our recent work has successfully designed the parallel variant of SAIS on a multicore machine, it remains a challenge to parallelize SACAK due to the strong data dependencies caused by the in-place constraint. A number of new techniques are proposed here to overcome the difficulties for designing pSACAK from the sequential SACAK. An experimental study is conducted to evaluate the performance of pSACAK versus other existing parallel suffix sorting algorithms. Our experimental results show that pSACAK is the most time and space efficient among all in comparison. To the best of our knowledge, pSACAK is the only linear-time and in-place parallel suffix sorting algorithm for constant alphabets reported so far.