A functional equation often arising in the analysis of algorithms (extended abstract)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Height in a digital search tree and the longest phrase of the Lempel-Ziv scheme
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A multivariate view of random bucket digital search trees
Journal of Algorithms - Analysis of algorithms
Generalized Lempel-Ziv parsing scheme and its preliminary analysis of the average profile
DCC '95 Proceedings of the Conference on Data Compression
TestU01: A C library for empirical testing of random number generators
ACM Transactions on Mathematical Software (TOMS)
On lempel-ziv complexity of sequences
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
Approximate counting with m counters: A detailed analysis
Theoretical Computer Science
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This paper studies the asymptotics of the variance for the internal path length in a symmetric digital search tree under the Bernoulli model. This problem has been open until now. It is proved that the variance is asymptotically equal to $N\cdot0.26600 +N\cdot\delta(\log_2 N),$ where $N$ is the number of stored records and $\delta(x)$ is a periodic function of mean zero and a very small amplitude. This result completes a series of studies devoted to the asymptotic analysis of the variances of digital tree parameters in the symmetric case. In order to prove the previous result a number of nontrivial problems concerning analytic continuations and some others of a numerical nature had to be solved. In fact, some of these techniques are motivated by the methodology introduced in an influential paper by Flajolet and Sedgewick.