G. H. Gonnet and J. I. Munro, The analysis of linear probing sort by the use of a new mathematical transform, Journal of Algorithms, 5:451--470 (1984).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....888# 313 where r = m # 1. Note that this expansion can also be obtained from (3) but with more involved computations. 2.3 Poissonization Poissonization is a widely used technique in stochastic process, summability of divergent sequence, analysis of algorithms, etc. see, for example, [1, 6, 18, 35, 19]. The idea is roughly described as follows. Given a discrete probability distribution k#0 (or, in general, a complex sequence) consider the Poisson generating function: b(#) e # a j C) The usual Poisson heuristic reads: If the sequence k#0 is smooth enough, then a n ....

G. H. Gonnet and J. I. Munro, The analysis of linear probing sort by the use of a new mathematical transform, Journal of Algorithms, 5:451--470 (1984).

....888 313 where r = m= 1. Note that this expansion can also be obtained from (3) but with more involved computations. 2.3 Poissonization Poissonization is a widely used technique in stochastic process, summability of divergent sequence, analysis of algorithms, etc. see, for example, [1, 6, 18, 35, 19]. The idea is roughly described as follows. Given a discrete probability distribution fa k g k0 (or, in general, a complex sequence) consider the Poisson generating function: b( e a j ( 2 C) The usual Poisson heuristic reads: If the sequence fa k g k0 is smooth enough, then a ....

G. H. Gonnet and J. I. Munro, The analysis of linear probing sort by the use of a new mathematical transform, Journal of Algorithms, 5:451--470 (1984).

....algorithms[3, 8] particularly in the way the behavior for a pivot of rank ffN can be derived from that of the median case, much like the analysis for sparse hash tables is a byproduct of the analysis for almost full tables. Also, lemma 2 bears great similarity to the Poisson Approximation Theorem[5, 7]. We leave as an open problem the determination of higher cumulants for the median case, to prove or disprove that the limit distribution is also Gaussian in the median case. Another interesting line of investigation is the study of the transition that leads to the appearance of the Theta( p n) ....

G.H. Gonnet and J.I. Munro. The analysis of linear probing sort by the use of a new mathematical transform. Journal of Algorithms, 5:451--470, 1984.

....alogorithm, to much time will be spent on this. The addresses that are to be sorted are nicely distributed, as we will discuss later, over the memory, a sorting algorithm, linear in the number of elements on the average can be used. We use the Linear Probing Sort method, discussed and analysed in [GM84]. Since we now know n we will not use all n 0 entries of the table only n=ff C entries will be used for the sorting phase. The technique used in this sorting algorithm is that the entry for an element is estimated among the n=ff entries. If there is a conflict in an entry, that is, two elements ....

....drawbacks. With a small amount of extra space, garbage collection is performed in time and space proportional to the reachable objects in the memory. We have analysed the behaviour of the algorithm in the average case under certain assumptions, relating the analysis to that of Gonnet and Munro in [GM84]. We have argued for the assumptions to be realistic, and the performance of the algorithm seems to support those assumptions. Our believe is that this algorithm, is both of practical and theoretical significance. ....

G.H. Gonnet and J.I. Munro. The Analysis of Linear Probing Sort by the Use of a New Mathematical Transform. Journal of Algorithms, XX(5):451--470, 1984.

....poissonized distribution for the height. Finally, we depoissonize these findings to recover our results for the original model. 3. 1 Poissonization and Depoissonization It is well known that often poissonization leads to a simpler solution due to unique properties of the Poisson distribution (cf. [9]) Poissonization is a technique which INRIA Analysis of an Asymmetric Leader Election Algorithm 9 replaces the fixed population model (sometimes called the Bernoulli model) by a model in which the population varies according to the Poisson law (hence, Poisson model) In the case of the leader ....

Gonnet, G. and Munro, J. The Analysis of Linear Probing Sort by the Use of a New Mathematical Transform, Journal of Algorithms, 5, 451-470, 1984.

....poissonized distribution for the height. Finally, we depoissonize these findings to recover our results for the original model. 3. 1 Poissonization and Depoissonization It is well known that often poissonization leads to a simpler solution due to unique properties of the Poisson distribution (cf. [9]) Poissonization is a technique which replaces the fixed population model (sometimes called the Bernoulli model) by a model in which the population varies according to the Poisson law (hence, Poisson model) In the case of the leader election algorithm, we replace n by a random variable N ....

Gonnet, G. and Munro, J. The Analysis of Linear Probing Sort by the Use of a New Mathematical Transform, Journal of Algorithms, 5, 451-470, 1984.

....poissonized distribution for the height. Finally, we depoissonize these findings to recover our results for the original model. 3. 1 Poissonization and Depoissonization It is well known that often poissonization leads to a simpler solution due to unique properties of the Poisson distribution (cf. [9]) Poissonization is a technique which replaces the fixed population model (sometimes called the Bernoulli model) by a model in which the population varies according to the Poisson law (hence, Poisson model) In the case of the leader election algorithm, we replace n by a random variable N ....

Gonnet, G. and Munro, J. The Analysis of Linear Probing Sort by the Use of a New Mathematical Transform, Journal of Algorithms, 5, 451-470, 1984.

....fill up all urns, etc. It is easy to see that the occupancy of urns are not independent (e.g. think all of balls falling into one urn, thus we know that all the remaining urns are empty) To overcome this difficulty an interesting probabilistic technique called poissonization was suggested (cf. [1, 8, 9, 17]) This work was partially supported by NATO Collaborative Grant CRG.950060. additional support by the Esprit Basic Research Action No. 7141 (Alcom II) y Additionally support by NSF Grants NSF CCR 9201078, NCR 9206315 and NCR 9415491. Namely, it is assumed that balls are generated by ....

....problems since one has to extract the original results from the Poisson model (i.e. depoissonize) To the best of our knowledge, poissonization was introduced by Marek Kac [17] a half a century ago when investigating deviations between theoretical and empirical distributions. Gonnet and Munro [8] introduced the Poisson transform to the field of the analysis of algorithms. Recently, poissonization was further popularized in the context of analysis of algorithms and combinatorial structures by Aldous [1] Fill et al. 3] Gonnet [7] Holst [9] Jacquet and R egnier [10, 11, 27] Jacquet ....

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G. Gonnet and J. Munro, The Analysis of Linear Probing Sort by the Use of a New Mathematical Transform, Journal of Algorithms, 5, 451-470, 1984.

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Gonnet, G. and Munro, J. The Analysis of Linear Probing Sort by the Use of a New Mathematical Transform, Journal of Algorithms, 5, 451-470, 1984.

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Gonnet, G. and Munro, J. (1984). The analysis of linear probing sort by the use of a new mathematical transform. J. of Algorithms, vol. 5, pp. 451--470.

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