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This article presents an O ( n )-time algorithm called SACA-K for sorting the suffixes of an input string T [0, n -1] over an alphabet A [0, K -1]. The problem of sorting the suffixes of T is also known as constructing the suffix array (SA) for T . The theoretical memory usage of SACA-K is n log K + n log n + K log n bits. Moreover, we also have a practical implementation for SACA-K that uses n bytes + ( n + 256) words and is suitable for strings over any alphabet up to full ASCII, where a word is log n bits. In our experiment, SACA-K outperforms SA-IS that was previously the most time- and space-efficient linear-time SA construction algorithm (SACA). SACA-K is around 33% faster and uses a smaller deterministic workspace of K words, where the workspace is the space needed beyond the input string and the output SA. Given K = O (1), SACA-K runs in linear time and O (1) workspace. To the best of our knowledge, such a result is the first reported in the literature with a practical source code publicly available.

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We present a new suffix array construction algorithm that aims to build, in external memory, the suffix array for an input string of length n measured in the magnitude of tens of Giga characters over a constant or integer alphabet. The core of this algorithm is adapted from the framework of the original internal memory SA-DS algorithm that samples fixed-size d-critical substrings. This new external-memory algorithm, called EM-SA-DS, uses novel cache data structures to construct a suffix array in a sequential scanning manner with good data spatial locality: data is read from or written to disk sequentially. On the assumed external-memory model with RAM capacity Ω (( nB ) 0.5 ), disk capacity O ( n ), and size of each I/O block B , all measured in log n -bit words, the I/O complexity of EM-SA-DS is O ( n / B ). This work provides a general cache-based solution that could be further exploited to develop external-memory solutions for other suffix-array-related problems, for example, computing the longest-common-prefix array, using a modern personal computer with a typical memory configuration of 4GB RAM and a single disk.

We present in this article an external memory algorithm, called disk SA-IS (DSA-IS), to exactly emulate the induced sorting algorithm SA-IS previously proposed for sorting suffixes in RAM. DSA-IS is a new diskfriendly method for sequentially retrieving the preceding character of a sorted suffix to induce the order of the preceding suffix. For a size-n string of a constant or integer alphabet, given the RAM capacity ((nW ) 0.5 ), where W is the size of each I/O buffer that is large enough to amortize the overhead of each access to disk, both the CPU time and peak disk use of DSA-IS are O(n). Our experimental study shows that on average, DSA-IS achieves the best time and space results of all of the existing external memory algorithms based on the induced sorting principle.