High-order entropy-compressed text indexes
Roberto Grossi, Ankur Kumar Gupta, Jeffrey Scott Vitter · 2003
We present a novel implementation of compressed suffix arrays exhibiting new tradeoffs between search time and space occupancy for a given text (or sequence) of n symbols over an alphabet , where each symbol is encoded by lg|Σ| bits. We show that compressed suffix arrays use just nH_h + O(n lg lg n/lg_|Σ| n) bits, while retaining full text indexing functionalities, such as searching any pattern sequence of length m in O(m lg|Σ| + polylog(n)) time. The term H_h ≤ lg|Σ| denotes the hth-order empirical entropy of the text, which means that our index is nearly optimal in space apart from lower-order terms, achieving asymptotically the empirical entropy of the text (with a multiplicative constant 1). If the text is highly compressible so that H_h = o(1) and the alphabet size is small, we obtain a text index with o(m) search time that requires only o(n) bits. Further results and tradeoffs are reported in the paper.