Lempel Ziv Computation in Small Space (LZ-CISS)

Abstract

For both the Lempel Ziv 77-and 78-factorization we propose algorithms generating the respective factorization using (1 + ǫ)n lg n + O(n) bits (for any positive constant ǫ ≤ 1) working space (including the space for the output) for any text of size n over an integer alphabet in O n/ǫ 2 time.

Lempel-Ziv Computation in Compressed Space (LZ-CICS)

“…Since LZ78 factors are naturally represented in a trie, the so-called LZ trie, improving LZ78 computation can be done, among others, by using sophisticated trie implementations [9,10], or by superimposing the suffix tree with the suffix trie [11,12]. We follow the latter approach.…”

“…Passes. Like the LZ77 algorithm in [12], we divide our algorithms in several passes. In a pass, we visit the leaves of ST in text position order.…”

“…We follow the approach from [12]. Determining the witnesses is done in the following way: Reaching the root from a leaf corresponding to a factor (while visiting only non-marked nodes) means that we found a fresh factor.…”

“…[12, Lemma 4]). Let e = (u, v) be an ST edge, and u the parent of the node v. Then n v ≤ min (c(e), s), where s is the number of leaves of the subtree rooted at v.…”

Faster Lightweight Lempel-Ziv Parsing

“…It is known that this is the best possible time for the general alphabets [14]. However, for the most important case of integer alphabet, there exist algorithms working in O(n) time and O(n log n) bits (see [8] for references). When σ is small, this number of bits is too big compared to the n log σ bits of the input string and can be prohibitive.…”