On Compressing Compact Suffix Arrays

Veli Mäkinen and Gonzalo Navarro

The compact suffix array (CSA) is a space-efficient full-text index, which is fast in practice to search for patterns in a static text. Compared to other compressed suffix arrays (Grossi and Vitter, Sadakane, Ferragina and Manzini), the CSA is significantly larger (1.6 times the text size, as opposed to 0.3-0.8 of compressed suffix arrays). Worse than that, the CSA needs the text separately available, while compressed suffix arrays include the text, that is, they are self-indexes. However, although compressed suffix arrays are very fast to determine the number of occurrences of a pattern, they are in practice very slow to report even a few occurrence positions or text contexts. In this aspect the CSA is much faster. In this paper we contribute to this space-time tradeoff by introducing the Compressed CSA (CCSA), a self-index that improves the space usage of the CSA in exchange for search speed. The main idea is to add small extra data structures that permit searching and displaying the text without actually accessing it, so the text can be deleted. We show that the occ occurrence positions of a pattern of length m in a text of length n can be reported in O((m+occ)*log n) time using the CCSA, whose representation needs O(n(1+H_k*log n)) bits for any k, H_k being the k-th order empirical entropy of the text. In practice the CCSA takes 1.23 times the text size (and includes the text). This is still larger than current compressed suffix arrays, and similar in size to the LZ-index of Navarro. Search times, however, are by far better than any existing self-index, except for reporting text contexts of occurrences, where the LZ-index is still superior.