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- Hsien-Kuei Hwang, Michael Fuchs, Vytas Zacharovas
- Discrete Mathematics & Theoretical Computer…
- 2010

Asymptotics of the variances of many cost measures in random digital search trees are often notoriously messy and involved to obtain. A new approach is proposed to facilitate such an analysis for several shape parameters on random symmetric digital search trees. Our approach starts from a more careful normalization at the level of Poisson generating… (More)

- Michael Fuchs, Hsien-Kuei Hwang, Vytas Zacharovas
- Theor. Comput. Sci.
- 2014

We develop analytic tools for the asymptotics of general trie statistics, which are particularly advantageous for clarifying the asymptotic variance. Many concrete examples are discussed for which new Fourier expansions are given. The tools are also useful for other splitting processes with an underlying binomial distribution. We specially highlight… (More)

Asymptotics of the variances of many cost measures in random digital search trees are often notoriously messy and involved to obtain. A new approach is proposed to facilitate such an analysis for several shape parameters on random symmetric digital search trees. Our approach starts from a more careful normalization at the level of Poisson generating… (More)

- Vytas Zacharovas
- 2009

Acknowledgments I would like to express my sincere gratitude to Professor E. Manstavičius for his attention to this work as well as for his help and advices. I would also like to thank the other members of the doctoral committee for their agreeing to participate in the defence of this work.

- VYTAS ZACHAROVAS
- 2013

We analyze the cost used by a naive exhaustive search algorithm for finding a maximum independent set in random graphs under the usual G n;p-model where each possible edge appears independently with the same probability p. The expected cost turns out to be of the less common asymptotic order n c log n , which we explore from several different perspectives.… (More)

A new approach to Poisson approximation is proposed. The basic idea is very simple and based on properties of the Charlier polynomials and the Parseval identity. Such an approach quickly leads to new effective bounds for several Poisson approximation problems. A selected survey on diverse Poisson approximation results is also given.

New uniform asymptotic approximations with error bounds are derived for a generalized total variation distance of Poisson approximations to the Poisson-binomial distribution. The method of proof is also applicable to other Poisson approximation problems.

- Vytas Zacharovas
- 2008

We investigate the summability in sense of Cesàro and its applications to investigation of the mean values of multiplicative functions on permutations.

- Cyril Banderier, Hsien-Kuei Hwang, Vlady Ravelomanana, Vytas Zacharovas
- SIAM J. Discrete Math.
- 2014

We analyze the cost used by a naive exhaustive search algorithm for finding a maximum independent set in random graphs under the usual G n;p-model where each possible edge appears independently with the same probability p. The expected cost turns out to be of the less common asymptotic order n c log n , which we explore from several different perspectives.… (More)

- Hsien-Kuei Hwang, Vytas Zacharovas
- Random Struct. Algorithms
- 2015

We consider sequences of random variables whose probability generating functions have only roots on the unit circle, which has only been sporadically studied in the literature. We show that the random variables are asymptotically normally distributed if and only if the fourth central and normalized (by the standard deviation) moment tends to 3, in contrast… (More)