A locally adaptive data compression scheme
Communications of the ACM
Robust transmission of unbounded strings using Fibonacci representations
IEEE Transactions on Information Theory
ACM Computing Surveys (CSUR)
Arithmetic coding for data compression
Communications of the ACM
Robust universal complete codes for transmission and compression
Discrete Applied Mathematics
ACM Transactions on Information Systems (TOIS)
An analysis of the Burrows—Wheeler transform
Journal of the ACM (JACM)
Second step algorithms in the Burrows-Wheeler compression algorithm
Software—Practice & Experience
Introduction to Algorithms
Boosting textual compression in optimal linear time
Journal of the ACM (JACM)
The engineering of a compression boosting library: theory vs practice in BWT compression
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Paging and list update under bijective analysis
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
An Application of Self-organizing Data Structures to Compression
SEA '09 Proceedings of the 8th International Symposium on Experimental Algorithms
List update with locality of reference
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Move-to-front, distance coding, and inversion frequencies revisited
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
Paging and list update under bijective analysis
Journal of the ACM (JACM)
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In this paper we present a new technique for worst-case analysis of compression algorithms which are based on the Burrows-Wheeler Transform. We deal mainly with the algorithm purposed by Burrows and Wheeler in their first paper on the subject [6], called bw0. This algorithm consists of the following three steps: 1) Compute the Burrows-Wheeler transform of the text, 2) Convert the transform into a sequence of integers using the move-to-front algorithm, 3) Encode the integers using Arithmetic code or any order-0 encoding (possibly with run-length encoding). We prove a strong upper bound on the worst-case compression ratio of this algorithm. This bound is significantly better than bounds known to date and is obtained via simple analytical techniques. Specifically, we show that for any input string s, and μ 1, the length of the compressed string is bounded by μ|s| Hk(s) + log(ζ(μ)) |s| + gk where Hk is the k-th order empirical entropy, gk is a constant depending only on k and on the size of the alphabet, and $\zeta(\mu) = \frac{1}{1^\mu} + \frac{1}{2^\mu} + \ldots $ is the standard zeta function. As part of the analysis we prove a result on the compressibility of integer sequences, which is of independent interest. Finally, we apply our techniques to prove a worst-case bound on the compression ratio of a compression algorithm based on the Burrows-Wheeler transform followed by distance coding, for which worst-case guarantees have never been given. We prove that the length of the compressed string is bounded by 1.7286 |s| Hk(s) + gk. This bound is better than the bound we give for bw0.