Succinct Text Indexes on Large Alphabet

In this paper, we first consider some properties of strings who have the same suffix array. Next, we design a data structure to support rank and select operations on an alphabet Σ using nlog|Σ| + (nlog|Σ|) bits in O(log|Σ|) time for a text of length n. It also supports an extended rank, namely rank≤, such that rank$^{\rm \leq}_{\alpha}$(T,i) returns the number of letters which are smaller than α in string T, plus the number of αs up to position i. Also, it runs in O(log|Σ|) time. By this structure, we implement the DAWG succinctly. The main structure only takes nlog|Σ| + o(nlog|Σ|) bits and supports basic operations of DAWG efficiently.

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