Lyndon factorization and Lempel-Ziv (LZ) factorization are both important tools for analysing the structure and complexity of strings, but their combinatorial structure is very different. In this paper, we establish the first direct connection between the two by showing that while the Lyndon factorization can be bigger than the non-overlapping LZ factorization (which we demonstrate by describin...

The properties of photonic quasicrystals ultimate rely on their inherent long-range order, a hallmark that can be quantified in many ways depending on the specific aspects to be studied. We use the Lempel-Ziv measure, a basic tool for information theoretic problems, to characterize the complexity of the specific structure under consideration. Using the generalized Fibonacci quasicrystals as our...

We give two optimal linear-time algorithms for computing the Longest Previous Factor (LPF) array corresponding to a string w. For any position i in w, LPF[i] gives the length of the longest factor of w starting at position i that occurs previously in w. Several properties and applications of LPF are investigated. They include computing the Lempel-Ziv factorization of a string and detecting all ...

we extend some results of Lempel and Restive on multiset decipherable codes to set decipherable codes. @ 2001 Elsevier Science Ltd. All rights reserved. Keywords-Codes, Unique decipherability, Multiset decipherability, Dominoes, Set decipherability.

The Lempel-Ziv algorithms are well-known dynamic dictionary algorithms of use in data compression. The talk shows how analytic models originally developed for the analysis of tries and digital search trees may be used to characterize their compression characteristics.

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Recent advances in biotechnology and web technology are generating huge collections of similar strings. People now face the problem of storing them compactly while supporting fast pattern searching. One compression scheme called relative Lempel-Ziv compression uses textual substitutions from a reference text as follows: Given a (large) set S of strings, represent each string in S as a concatena...