Redundancy of the Lempel-Ziv incremental parsing rule

Redundancy of the Lempel-Ziv incremental parsing rule

The Lempel-Ziv codes are universal variable-tofixed length codes that have become virtually standard in practical lossless data compression. For any given source output string from a Markov or unifilar source, we upper-bound the difference between the number of binary digits needed to encode the string and the self-information of the string. We use this result to demonstrate that for unifilar o...

Lightweight Lempel-Ziv Parsing

We introduce a new approach to LZ77 factorization that uses O(n/d) words of working space and O(dn) time for any d ≥ 1 (for polylogarithmic alphabet sizes). We also describe carefully engineered implementations of alternative approaches to lightweight LZ77 factorization. Extensive experiments show that the new algorithm is superior in most cases, particularly at the lowest memory levels and for...

Faster Lightweight Lempel-Ziv Parsing

We present an algorithm that computes the Lempel-Ziv decomposition in O(n(log σ+log log n)) time and n log σ+ǫn bits of space, where ǫ is a constant rational parameter, n is the length of the input string, and σ is the alphabet size. The n log σ bits in the space bound are for the input string itself which is treated as read-only.

Range Predecessor and Lempel-Ziv Parsing

The Lempel-Ziv parsing of a string (LZ77 for short) is one of the most important and widely-used algorithmic tools in data compression and string processing. We show that the LempelZiv parsing of a string of length n on an alphabet of size σ can be computed in O(n log log σ) time (O(n) time if we allow randomization) using O(n log σ) bits of working space; that is, using space proportional to t...

Improved redundancy of a version of the Lempel-Ziv algorithm