Efficient LZ78 factorization of grammar compressed text

We present an efficient algorithm for computing the LZ78 factorization of a text, where the text is represented as a straight line program (SLP), which is a context free grammar in the Chomsky normal form that generates a single string. Given an SLP of size $n$ representing a text $S$ of length $N$, our algorithm computes the LZ78 factorization of $T$ in $O(n\sqrt{N}+m\log N)$ time and $O(n\sqrt{N}+m)$ space, where $m$ is the number of resulting LZ78 factors. We also show how to improve the algorithm so that the $n\sqrt{N}$ term in the time and space complexities becomes either $nL$, where $L$ is the length of the longest LZ78 factor, or $(N - \alpha)$ where $\alpha \geq 0$ is a quantity which depends on the amount of redundancy that the SLP captures with respect to substrings of $S$ of a certain length. Since $m = O(N/\log_\sigma N)$ where $\sigma$ is the alphabet size, the latter is asymptotically at least as fast as a linear time algorithm which runs on the uncompressed string when $\sigma$ is constant, and can be more efficient when the text is compressible, i.e. when $m$ and $n$ are small.Comment: SPIRE 201

Practical Evaluation of Lempel-Ziv-78 and Lempel-Ziv-Welch Tries

We present the first thorough practical study of the Lempel-Ziv-78 and the Lempel-Ziv-Welch computation based on trie data structures. With a careful selection of trie representations we can beat well-tuned popular trie data structures like Judy, m-Bonsai or Cedar

New Algorithms for Position Heaps

We present several results about position heaps, a relatively new alternative to suffix trees and suffix arrays. First, we show that, if we limit the maximum length of patterns to be sought, then we can also limit the height of the heap and reduce the worst-case cost of insertions and deletions. Second, we show how to build a position heap in linear time independent of the size of the alphabet. Third, we show how to augment a position heap such that it supports access to the corresponding suffix array, and vice versa. Fourth, we introduce a variant of a position heap that can be simulated efficiently by a compressed suffix array with a linear number of extra bits

From LZ77 to the run-length encoded burrows-wheeler transform, and back

The Lempel-Ziv factorization (LZ77) and the Run-Length encoded Burrows-Wheeler Transform (RLBWT) are two important tools in text compression and indexing, being their sizes z and r closely related to the amount of text self-repetitiveness. In this paper we consider the problem of converting the two representations into each other within a working space proportional to the input and the output. Let n be the text length. We show that RLBW T can be converted to LZ77 in O(n log r) time and O(r) words of working space. Conversely, we provide an algorithm to convert LZ77 to RLBW T in O n(log r + log z) time and O(r + z) words of working space. Note that r and z can be constant if the text is highly repetitive, and our algorithms can operate with (up to) exponentially less space than naive solutions based on full decompression

A new word-based compression model allowing compressed pattern matching

In this study a new semistatic data compression model that has a fast coding process and that allows compressed pattern matching is introduced. The name of the proposed model is chosen as tagged word-based compression algorithm (TWBCA) since it has a word-based coding and word-based compressed matching algorithm. The model has two phases. In the first phase a dictionary is constructed by adding a phrase, paying attention to word boundaries, and in the second phase compression is done by using codewords of phrases in this dictionary. The first byte of the codeword determines whether the word is compressed or not. By paying attention to this rule, the CPM process can be conducted as word based. In addition, the proposed method makes it possible to also search for the group of consecutively compressed words. Any of the previous pattern matching algorithms can be chosen to use in compressed pattern matching as a black box. The duration of the CPM process is always less than the duration of the same process on the texts coded by Gzip tool. While matching longer patterns, compressed pattern matching takes more time on the texts coded by compress and end-tagged dense code (ETDC). However, searching shorter patterns takes less time on texts coded by our approach than the texts compressed with compress. Besides this, the compression ratio of our algorithm has a better performance against ETDC only on a file that has been written in Turkish. The compression performance of TWBCA is stable and does not vary over 6% on different text files