An Alphabet-Friendly FM-Index

We show that, by combining an existing compression boosting technique with the wavelet tree data structure, we are able to design a variant of the FM-index which scales well with the size of the input alphabet Σ. The size of the new index built on a string T [1, n] is bounded by nHk(T )+O ( (n log log n)/ log|Σ| n ) bits, where Hk(T ) is the k-th order empirical entropy of T . The above bound holds simultaneously for all k ≤ α log|Σ| n and 0 < α < 1. Moreover, the index design does not depend on the parameter k, which plays a role only in analysis of the space occupancy. Using our index, the counting of the occurrences of an arbitrary pattern P [1, p] as a substring of T takes O(p log |Σ|) time. Locating each pattern occurrence takes O(log |Σ| (log n/ log log n)) time. Reporting a text substring of length l takes O((l+ log n/ log log n) log |Σ|) time.