Reducing the Space Requirement of LZ-Index

The LZ-index is a compressed full-text self-index able to represent a text T1...u, over an alphabet of size σ = O(polylog(u)) and with k-th order empirical entropy Hk(T ), using 4uHk(T )+ o(u logσ) bits for any k = o(logσ u). It can report all the occ occurrences of a pattern P1...m in T in O(m3 logσ +(m + occ) log u) worst case time. Its main drawback is the factor 4 in its space complexity, which makes it larger than other state-of-the-art alternatives. In this paper we present two different approaches to reduce the space requirement of LZ-index. In both cases we achieve (2 + ε)uHk(T )+ o(u logσ) bits of space, for any constant ε > 0, and we simultaneously improve the search time to O(m2 logm + (m + occ) log u). Both indexes support displaying any subtext of length l in optimal O(l/ logσ u) time. In addition, we show how the space can be squeezed to (1+ ε)uHk(T )+o(u log σ) to obtain a structure with O(m2) average search time for m > 2logσ u.