Bernhard Balkenhol

Modifications of the Burrows and Wheeler data compression algorithm

We improve upon previous results on the Burrows and Wheeler (BW)-algorithm. Based on the context tree model, we consider the specific statistical properties of the data at the output of the BWT. We describe six important properties, three of which have not been described elsewhere. These considerations lead to modifications of the coding method, which in turn improve the coding efficiency. We briefly describe how to compute the BWT with low complexity in time and space, using suffix trees in two different representations. Finally, we present experimental results about the compression rate and running time of our method, and compare these results to previous achievements.

Universal data compression based on the Burrows-Wheeler transformation: theory and practice

A very interesting recent development in data compression is the Burrows-Wheeler Transformation. The idea is to permute the input sequence in such a way that characters with a similar context are grouped together. We provide a thorough analysis of the Burrows-Wheeler Transformation from an information theoretic point of view. Based on this analysis, the main part of the paper systematically considers techniques to efficiently implement a practical data compression program based on the transformation. We show that our program achieves a better compression rate than other programs that have similar requirements in space and time.

Space Efficient Linear Time Computation of the Burrows and Wheeler-Transformation

In [4] a universal data compression algorithm (BW-algorithm, for short) is described which achieves compression rates that are close to the best known rates achieved in practice. Due to its simplicity, the algorithm can be implemented with relatively low complexity. Recently [2] modified the BW-algorithm to improve the compression rate even further. For a thorough discussion on the information theoretic background of the BW-algorithm and more references, see [1]. The most time and space consuming part of the BW-algorithm is the Burrows and Wheeler-Transformation (BWT, for short), which permutes the input string in such a way that characters with a similar context are grouped together. In [4], it was observed that for an input string of length n, this transformation can be computed in O(n) time and space using suffix trees. However, suffix trees have a reputation of being very greedy for space, and therefore most researchers resorted to alternative non-linear methods for computing the BWT: The algorithm of [9] runs in O(n log n) worst case time and it requires 8n bytes of space. The algorithm of [3] is based on Quicksort. It is fast on average, but the worst case running time is O(n 2). The Benson-Sedgewick algorithm requires 4n bytes. Its running time can be improved in practice, for the cost of 4n extra bytes. Recently, [11] showed how to combine the Manber-Myers Algorithm with the Bentley-Sedgewick Algorithm, to achieve a method running in O(n log n) worst case time and using 9n bytes.

T-shift synchronization codes

Abstract In this paper we give a construction of T -shift synchronization codes, i.e. block codes capable of correcting synchronization shifts of length at most T in either direction (left or right). We prove lower and upper bounds on the maximal cardinality of such codes. An infinite number of the constructed codes turn to be asymptotically optimal.

A game tree with distinct leaf values which is easy for the alpha-beta algorithm

Abstract The alpha-beta algorithm is an efficient technique for searching game trees. As parallel computers become more available, it is important to have good parallel game tree search algorithms. Until now it is an open problem whether a linear speedup can be achieved with respect to sequential alpha-beta. This note presents a sample of game trees with distinct leaf values, which are easy for sequential alpha-beta—independently of the move ordering in the trees. We conjecture that these trees are difficult test cases for parallel algorithms.

A fast suffix-sorting algorithm

We present an algorithm to sort all suffixes of

A Fast Suffix-Sorting Algorithm

x^n=(x_1,\dots,x_n) \in {\cal X}^n

Identification for Sources

lexicographically, where

One attempt of a compression algorithm using the BWT

{\cal X}=\{0,\dots,q-1\}

Some properties of fix-free codes

. Fast and efficient sorting of a large amount of data according to its suffix structure (suffix-sorting) is a useful technology in many fields of application, front-most in the field of Data Compression where it is used e.g. for the Burrows and Wheeler Transformation (BWT for short), a block-sorting transformation ([3],[9]).