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
Limit laws for the height in PATRICIA tries
Journal of Algorithms - Analysis of algorithms
Additive Decompositions, Random Allocations, and Threshold Phenomena
Combinatorics, Probability and Computing
Concentration of Size and Path Length of Tries
Combinatorics, Probability and Computing
On the number of full levels in tries
Random Structures & Algorithms
Towards a complete characterization of tries
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Partial fillup and search time in LC tries
ACM Transactions on Algorithms (TALG)
Probability in the Engineering and Informational Sciences
Inverse auctions: Injecting unique minima into random sets
ACM Transactions on Algorithms (TALG)
Broadcast delay of epidemic routing in intermittently connected networks
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Sharp bounds on the entropy of the poisson law and related quantities
IEEE Transactions on Information Theory
On space-time capacity limits in mobile and delay tolerant networks
INFOCOM'10 Proceedings of the 29th conference on Information communications
Information propagation speed in mobile and delay tolerant networks
IEEE Transactions on Information Theory
Average case analysis of algorithms
Algorithms and theory of computation handbook
The expected profile of digital search trees
Journal of Combinatorial Theory Series A
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
ASIAN'04 Proceedings of the 9th Asian Computing Science conference on Advances in Computer Science: dedicated to Jean-Louis Lassez on the Occasion of His 5th Cycle Birthday
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In combinatorics and analysis of algorithms a Poisson version of aproblem (henceforth called a Poissonmodel orpoissonization) is often easier tosolve than the original one, which we name here theBernoulli model. Poissonization is atechnique that replaces the original input (e.g., think of balls throwninto urns) by a Poisson process (e.g., think of balls arriving accordingto a Poisson process into urns). More precisely, analytical Poissontransform maps a sequence (e.g., characterizing the Bernoulli model)into a generating function of a complex variable. However, afterpoissonization one must depoissonizein order to translate the results of the Poisson model into theoriginal (i.e., Bernoulli) model. We present in this paper severalanalytical depoissonization results that fall into the following generalscheme: If the Poisson transform has an appropriategrowth in the complex plane, then an asymptotic expansion of thesequence can be expressed in terms of the Poisson transform and itsderivatives evaluated on the real line. Notsurprisingly, actual formulations of depoissonization results depend onthe nature of the growth of the Poisson transform, and thus we havepolynomial andexponential depoissonizationtheorems. Normalization (e.g., as in the central limit theorem)introduces another twist that led us to formulate the so-calleddiagonal depoissonization theorems.Finally, we illustrate our results on numerous examples fromcombinatorics and the analysis of algorithms and data structures (e.g.,combinatorial assemblies, digital trees, multiaccess protocols,probabilistic counting, selecting a leader, data compression,etc.).—Authors' Abstract