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Title Implementing the LZ-index: Theory versus Practice
Authors Gonzalo Navarro
Publication date February 2009
Abstract 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 $\sigma$ 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 $O(m^3 \log\sigma + (m+R)\log n)$. 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
$O(\sigma m\log u + \sqrt{uR})$. 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.
Pages article 2
Volume 13
Journal name ACM Journal of Experimental Algorithmics
Publisher ACM Press (New York, NY, USA)
Reference URL View reference page