To construct the su x array of a string S boils down to sorting all su xes of S in lexicographic order (also known as alphabetical order, dictionary order, or lexical order). This order is induced by an order on the alphabet Σ. In this manuscript, Σ is an ordered alphabet of constant size σ. It is sometimes convenient to regard Σ as an array of size σ so that the characters appear in ascending ...

High-throughput sequencing technologies make it possible to rapidly acquire large numbers of individual genomes, which, for a given organism, vary only slightly from one to another. Such repetitive and large sequence collections are a unique challange for compression. In previous work we described the RLZ algorithm, which greedily parses each genome into factors, represented as position and len...

We present new algorithms for the sliding window Lempel-Ziv (LZ77) problem and the approximate rightmost LZ77 parsing problem. Our main result is a new and surprisingly simple algorithm that computes the sliding window LZ77 parse in O(w) space and either O(n) expected time or O(n log logw + z log log σ) deterministic time. Here, w is the window size, n is the size of the input string, z is the ...

Spike train analysis generally focuses on two aims: (1) the estimate of the neuronal information quantity, and (2) the quantification of spikes or bursts synchronization. We introduce here a new multivariate index based on LempelZiv complexity for spike train analysis. This index, called mutual Lempel-Ziv complexity (MLZC), can both measure spikes correlations and estimate the information carri...

We explore the possibility of transforming the standard encodings of the main LZ methods to be of fixed length, without reverting to the originally suggested encodings. This has the advantage of allowing easier processing and giving more robustness against errors, while only marginally reducing the compression efficiency in certain cases.

Given two strings (a text t of length n and a pattern p) and a natural number w, window subsequence problems consist in deciding whether p occurs as a subsequence of t and/or finding the number of size (at most) w windows of text t which contain pattern p as a subsequence, i.e. the letters of pattern p occur in the text window, in the same order as in p, but not necessarily consecutively (they ...

In this paper we compare the difference in performance of two Prediction by Partial Matching (PPM) family compressors (PPM$^*$ and original Bounded PPM algorithm) Lempel-Ziv 78 (LZ) algorithm. We construct an infinite binary sequence whose worst-case compression ratio for PPM$^*$ is $0$, while PPM's LZ's best-case ratios are at least $1/2$ $1$ respectively. This enumeration all strings order le...