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A Simple Alphabet-Independent FM-Index

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Szymon Grabowski, Gonzalo Navarro, Rafal Przywarski, Alejandro Salinger,
and Veli Mäkinen

We design a succinct full-text index based on the idea of Huffman-compressing
the text and then applying the Burrows-Wheeler transform over it. The resulting
structure can be searched as an FM-index, with the benefit of removing the sharp
dependence on the alphabet size, *s*, present in that structure. On a text
of length *n* with zero-order entropy *H0*, our index needs
*O(n(H0+1))* bits of space, without any significant dependence on *s*.
The average search time for a pattern of length *m* is *O(m(H0+1))*,
under reasonable assumptions. Each position of a text occurrence can be located
in worst case time *O((H0+1) log n)*, while any text substring of length
*L* can be retrieved in
*O((H0+1)L)* average time in addition to the previous worst case time.
Our index provides a relevant space/time tradeoff between existing succinct
data structures, with the additional interest of being easy to implement.
We also explore other coding variants alternative to Huffman and exploit their
synchronization properties. Our experimental results on various types of texts
show that our indexes are highly competitive in the space/time tradeoff map.