Implementing the LZ-index: Theory versus Practice

Gonzalo Navarro

The LZ-index is a theoretical proposal of a lightweight data structure for text indexing, based on the Ziv-Lempel trie. If a text of u characters over an alphabet of size s is compressible to n symbols using the LZ78 algorithm, then the LZ-index takes 4n log_2(n) (1+o(1)) bits of space (that is, 4 times the entropy of the text) and reports the R occurrences of a pattern of length m in worst case time O(m^3 log(s) + (m+R) log n). In this paper we face the challenge of obtaining a practical implementation of the LZ-index, which is not at all straightforward from the theoretical proposal. We end up with a prototype that takes the promised space and has average search time O(s m log(u) + sqrt(uR)). This prototype is shown to be faster than other competing approaches when we take into account the time to report the positions or text contexts of the occurrences found. We show in detail the process of implementing the index, which involves interesting lessons of theory versus practice.