A theoretical and experimental study on the construction of suffix arrays in external memory

The construction of full-text indexes on very large text collections is nowadays a hot problem. The suffix array [Manber-Myers,~1993] is one of the most attractive full-text indexing data structures due to its simplicity, space efficiency and powerful/fast search operations supported. In this paper we analyze, both theoretically and experimentally, the I/O-complexity and the working space of six algorithms for constructing large suffix arrays. Three of them are the state-of-the-art, the other three algorithms are our new proposals. We perform a set of experiments based on three different data sets (English texts, Amino-acid sequences and random texts) and give a precise hierarchy of these algorithms according to their working-space vs. construction-time tradeoff. Given the current trends in model design~\cite{Farach-et-al,Vitter} and disk technology~\cite{quantum,Ruemmler-Wilkes}, we will pose particular attention to differentiate between ``random'' and ``contiguous'' disk accesses, in order to reasonably explain some practical I/O-phenomena which are related to the experimental behavior of these algorithms and that would be otherwise meaningless in the light of other simpler external-memory models. At the best of our knowledge, this is the first study which provides a wide spectrum of possible approaches to the construction of suffix arrays in external memory, and thus it should be helpful to anyone who is interested in building full-text indexes on very large text collections. Finally, we conclude our paper by addressing two other issues. The former concerns with the problem of building word-indexes; we show that our results can be successfully applied to this case too, without any loss in efficiency and without compromising the simplicity of programming so to achieve a uniform, simple and efficient approach to both the two indexing models. The latter issue is related to the intriguing and apparently counterintuitive ``contradiction'' between the effective practical performance of the well-known BaezaYates-Gonnet-Snider's algorithm~\cite{book-info}, verified in our experiments, and its unappealing (i.e., cubic) worst-case behavior. We devise a new external-memory algorithm that follows the basic philosophy underlying that algorithm but in a significantly different manner, thus resulting in a novel approach which combines good worst-case bounds with efficient practical performance