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We propose a new approach for calculating the Lempel-Ziv factorization of astring, based on run length encoding (RLE). We present a conceptually simpleoff-line algorithm based on a variant of suffix arrays, as well as an on-linealgorithm based on a variant of directed acyclic word graphs (DAWGs). Bothalgorithms run in $O(N+n\log n)$ time and O(n) extra space, where N is the sizeof the string, $n\leq N$ is the number of RLE factors. The time dependency on Nis only in the conversion of the string to RLE, which can be computed veryefficiently in O(N) time and O(1) extra space (excluding the output). When thestring is compressible via RLE, i.e., $n = o(N)$, our algorithms are, to thebest of our knowledge, the first algorithms which require only o(N) extra spacewhile running in $o(N\log N)$ time.

Time and Space Efficient Lempel-Ziv Factorization based on Run Length Encoding