On the asymptotic behavior of some algorithms

Pierpoint, Robert

doi:10.1002/rsa.20075

Cited by 7 publications

(12 citation statements)

References 18 publications

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“…Its proof is based on integral representations and Fubini's Theorem instead of complex analysis techniques as it is usually the case in the context of harmonic series. See Robert [15] for a presentation of these methods. Proposition 1.…”

Section: A Convergence Resultsmentioning

confidence: 99%

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Analysis of Steiner subtrees of random trees for traceroute algorithms

Guillemin

Pierpoint

2009

Random Struct Algorithms

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Abstract. We consider in this paper the problem of discovering, via a traceroute algorithm, the topology of a network, whose graph is spanned by an infinite branching process. A subset of nodes is selected according to some criterion. As a measure of efficiency of the algorithm, the Steiner distance of the selected nodes, i.e. the size of the spanning sub-tree of these nodes, is investigated. For the selection of nodes, two criteria are considered: A node is randomly selected with a probability, which is either independent of the depth of the node (uniform model) or else in the depth biased model, is exponentially decaying with respect to its depth. The limiting behavior the size of the discovered subtree is investigated for both models.

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Section: A Convergence Resultsmentioning

confidence: 99%

“…In Proposition 2, the expression of ρ (2) 2 (λ) is defined a priori only for a deterministic offspring distribution, but can be extended to any offspring distribution by using the right hand side of Equation (15). In the following, we study the behavior of ρ (2) 2 (λ) for an arbitrary offspring distribution.…”

Section: It Follows Thatmentioning

confidence: 99%

Analysis of Steiner subtrees of random trees for traceroute algorithms

Guillemin

Pierpoint

2009

Random Struct Algorithms

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“…Later on, Philippe Robert found that such oscillating asymptotic behavior is a typical feature of algorithms with a tree structure. For further reading I recommend his very interesting papers [9] and [12]. I think that the oscillating asymptotic behavior of algorithms is a highly compelling phenomenon, and I am very happy that our paper contributed in its study.…”

Section: Collecting N Items On a Circlementioning

confidence: 98%

Chapter 23 Applications: simple models and difficult theorems

Litvak

2011

Selected Works of Willem Van Zwet

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In this short article I will discuss three papers written by Willem van Zwet with three different co-authors: Mathisca de Gunst, Marta Fiocco, and myself. Each of the papers focuses on one particular application: growth of the number of biological cells [3], spreading of an infection [7], and the optimal travel time in warehousing carousel systems [8]. IntroductionIn this short article I will discuss three papers written by Willem van Zwet with three different co-authors: Mathisca de Gunst, Marta Fiocco, and myself. Each of the papers focuses on one particular application: growth of the number of biological cells [3], spreading of an infection [7], and the optimal travel time in warehousing carousel systems [8]. To my opinion, each of these papers displays the attitude that I personally value a lot in mathematics. An application is the strong starting point for each of the papers. Further, the model is simple and transparent. Yet, the analysis involves advanced mathematics and brings to the results that not only give new insights into the applications but also are of a pure mathematical interest. The present volume contains [7] and [8], and the follow-up paper [4] of [3] which I will also briefly discuss.The papers are written in a clear language and do not try to look more fancy than they are. In fact, I remember Willem laughing at my attempts to make the paper more general by replacing 112 with bE (0, 1): 'What have you done? Please, bring the 1/2 back! It is more natural and makes the whole thing much easier to read'. And on my sceptical remark about the number of people who are actually going to

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“…After some transformation, (2) is interpreted as a probabilistic equation which is iterated by using appropriate independent random variables. Following the method of Robert [38], the next step is to perform a probabilistic de-Poissonnization and, by using Fubini's theorem conveniently, to represent the quantity E(R n ) by using a Poisson point process on the real line. The final, crucial step which differs from [38], consists in using the key renewal theorem to get the asymptotic behavior of the sequence (E(R n )).…”

Section: Related Problemsmentioning

confidence: 99%

A probabilistic analysis of some tree algorithms

Mohamed¹,

Pierpoint²

2005

Ann. Appl. Probab.

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In this paper a general class of tree algorithms is analyzed. It is shown that, by using an appropriate probabilistic representation of the quantities of interest, the asymptotic behavior of these algorithms can be obtained quite easily without resorting to the usual complex analysis techniques. This approach gives a unified probabilistic treatment of these questions. It simplifies and extends some of the results known in this domain.Comment: Published at http://dx.doi.org/10.1214/105051605000000494 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

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On the asymptotic behavior of some algorithms

Cited by 7 publications

References 18 publications

Analysis of Steiner subtrees of random trees for traceroute algorithms

Analysis of Steiner subtrees of random trees for traceroute algorithms

Chapter 23 Applications: simple models and difficult theorems

A probabilistic analysis of some tree algorithms

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