We consider several basic problems for texts and show that if the input texts are given by their Lempel-Ziv codes then the problems can be solved deterministically in polynomial time in the case when the original (uncompressed) texts are of exponential size. The growing importance of massively stored information requires new approaches to algorithms for compressed texts without decompressing. D...

In many scenario of digital communication and data processing, we may deal with strings of data which have certain structural regularities, making it possible for time-saving techniques of data compression. Given a discrete data source, the data compression problem is first to identify the limitations of the source, and second to devise a coding scheme which will best compress it subject to cer...

We present a simple pedagogical graph theoretical description of Lempel, Even, and Cederbaum (LEC) planarity method based on concepts due to Thomas. A linear-time implementation of LEC method using the PC-tree data structure of Shih and Hsu is provided and described in details. We report on an experimental study involving this implementation and other available linear-time implementations of pl...

Simple and fast decoding is one of the main advantages of LZ77-type text encoding used in many popular file compressors such as gzip and 7zip. With the recent introduction of external memory algorithms for Lempel–Ziv factorization there is a need for external memory LZ77 decoding but the standard algorithm makes random accesses to the text and cannot be trivially modified for external memory co...

Let a text of u characters over an alphabet of size be compressible to n symbols by the LZ78 or LZW algorithm. We show that it is possible to build a data structure based on the Ziv-Lempel trie that takes 4n log 2 n(1 + o(1)) bits of space and reports the R occurrences of a pattern of length m in worst case time O(m 2 log(mm) + (m + R) log n).

The need to index and search huge highly repetitive sequence collections is rapidly arising in various fields, including computational biology, software repositories, versioned collections, and others. In this short survey we briefly describe the progress made along three research lines to address the problem: compressed suffix arrays, grammar compressed indexes, and Lempel-Ziv compressed indexes.

For both the Lempel Ziv 77and 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 )

These applications most commonly fall into the category of thin client architectures, screen teleconferencing and the recording of demonstration sequences. This paper explores the use of MMXTM and Streaming SIMD Extension (SSE) instructions [11,12] to improve the performance of a hybrid Lempel-Ziv [15] encoding algorithm with temporally seeded history buffer and predictive quarter-static range ...