Space Efficient Linear Time Lempel-Ziv Factorization for Small Alphabets

We present a new linear time algorithm for computing the Lempel-Ziv Factorization (LZ77) of a given string of length N on an alphabet of size sigma, that utilizes only N log N + O(sigma log N) bits of working space. When the alphabet size is small, this greatly improves the previous best space requirement for linear time LZ77 factorization (Karkkainen et al. CPM 2013), which is 2N log N bits, i.e. two integer arrays of length N. Experiments show that despite the added complexity of the algorithm, the speed of the algorithm is only around two to three times slower than previous fastest linear time algorithms.