A locally adaptive data compression scheme
Communications of the ACM
Digital search trees revisited
SIAM Journal on Computing
A characterization of digital search trees from the successful search viewpoint
Theoretical Computer Science
A generalized suffix tree and its (un)expected asymptotic behaviors
SIAM Journal on Computing
Digital Search Trees Again Revisited: The Internal Path Length Perspective
SIAM Journal on Computing
Asymptotic behavior of the Lempel-Ziv parsing scheme and digital search trees
Theoretical Computer Science - Special volume on mathematical analysis of algorithms (dedicated to D. E. Knuth)
Average profile and limiting distribution for a phrase size in the Lempel-Ziv parsing algorithm
IEEE Transactions on Information Theory
On the Average Redundancy Rate of the Lempel-Ziv Code with K-Error Protocol
DCC '00 Proceedings of the Conference on Data Compression
Quasi-distinct Parsing and Optimal Compression Methods
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Quasi-distinct parsing and optimal compression methods
Theoretical Computer Science
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The goal of this contribution is twofold: (i) to introduce a generalized Lempel-Ziv parsing scheme, and (ii) to analyze second-order properties of some compression schemes based on the above parsing scheme. We consider a generalized Lempel-Ziv parsing scheme that partitions a sequence of length n into variable phrases (blocks) such that a new block is the longest substring seen in the past by at most b-1 phrases. The case b=1 corresponds to the original Lempel-Ziv scheme. In this paper, we investigate the size of a randomly selected phrase, and the average number of phrases of a given size through analyzing the so called b-digital search tree (b-DST) representation. For a memoryless source, we prove that the size of a typical phrase is asymptotically normally distributed. This result is new even for b=1, and b