1,716 research outputs found

    Linear pattern matching on sparse suffix trees

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    Packing several characters into one computer word is a simple and natural way to compress the representation of a string and to speed up its processing. Exploiting this idea, we propose an index for a packed string, based on a {\em sparse suffix tree} \cite{KU-96} with appropriately defined suffix links. Assuming, under the standard unit-cost RAM model, that a word can store up to logσn\log_{\sigma}n characters (σ\sigma the alphabet size), our index takes O(n/logσn)O(n/\log_{\sigma}n) space, i.e. the same space as the packed string itself. The resulting pattern matching algorithm runs in time O(m+r2+rocc)O(m+r^2+r\cdot occ), where mm is the length of the pattern, rr is the actual number of characters stored in a word and occocc is the number of pattern occurrences

    Universal Compressed Text Indexing

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    The rise of repetitive datasets has lately generated a lot of interest in compressed self-indexes based on dictionary compression, a rich and heterogeneous family that exploits text repetitions in different ways. For each such compression scheme, several different indexing solutions have been proposed in the last two decades. To date, the fastest indexes for repetitive texts are based on the run-length compressed Burrows-Wheeler transform and on the Compact Directed Acyclic Word Graph. The most space-efficient indexes, on the other hand, are based on the Lempel-Ziv parsing and on grammar compression. Indexes for more universal schemes such as collage systems and macro schemes have not yet been proposed. Very recently, Kempa and Prezza [STOC 2018] showed that all dictionary compressors can be interpreted as approximation algorithms for the smallest string attractor, that is, a set of text positions capturing all distinct substrings. Starting from this observation, in this paper we develop the first universal compressed self-index, that is, the first indexing data structure based on string attractors, which can therefore be built on top of any dictionary-compressed text representation. Let γ\gamma be the size of a string attractor for a text of length nn. Our index takes O(γlog(n/γ))O(\gamma\log(n/\gamma)) words of space and supports locating the occocc occurrences of any pattern of length mm in O(mlogn+occlogϵn)O(m\log n + occ\log^{\epsilon}n) time, for any constant ϵ>0\epsilon>0. This is, in particular, the first index for general macro schemes and collage systems. Our result shows that the relation between indexing and compression is much deeper than what was previously thought: the simple property standing at the core of all dictionary compressors is sufficient to support fast indexed queries.Comment: Fixed with reviewer's comment
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