P. Grabner, Searching for losers, Random Structures and Algorithms, 4:99--110 (1993).  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 ....

P. Grabner, Searching for losers, Random Structures and Algorithms, 4:99--110 (1993).

....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 ....

P. Grabner, Searching for losers, Random Structures and Algorithms, 4:99--110 (1993). 19

....about the saddle point method, one can refer to [1] or to [10] As m(z) e m(z) where d is bounded, the previous saddle point is asymptotically not a ected by multiplying e by this in nite product. Thus we get m(n) and similarly m( n) Compare [4] for such an approach. We next study both terms of the sum by making use of the Mellin transform as in the previous instance. Theorem 3. In the instance of two dominant digits d 1 , d d , with d 1 = d d = dM , the nth moment M n of the Cantor (q; D) distribution has for n 1 the following ....

P. Grabner. Searching for losers. Random Structures and Algorithms, 4:99-110, 1993.

....a single winner (leader) is identified. If all players throw heads at any stage, the toss is inconclusive and all players participate again in the contest. How many tosses are needed to identify a winner The problem was posed for a fair (unbiased) coin tossing process by Prodinger [19] cf. also [10]) who provided the first non trivial analysis. Recently, for the same fair coin model, Fill et al. 5] find the limiting distribution for the number of rounds. In this paper, we analyze the same problem but when the coins involved are biased, that is, the probability p of throwing a head is not ....

....[18] for updated account on recent developments in this area. In fact, tries and other digital trees were used as a testbed for the precise analytical analysis of algorithms . Several new analytical techniques were developed in the process of analyzing different parameters of digital trees (cf. [4, 5, 10, 13, 14, 16, 20, 21, 22]) Recently, the focus of the research was moved towards developing analytical techniques that can handle limiting distributions and large deviations results (cf. 5, 11, 12, 14, 15] In this paper, we continue recent lines of research and establish asymptotic distribution together with the ....

[Article contains additional citation context not shown here]

Grabner, P. Searching for losers. Random Structures and Algorithms, 4, 99-- 110, 1993.

....a single winner (leader) is identified. If all players throw heads at any stage, the toss is inconclusive and all players participate again in the contest. How many tosses are needed to identify a winner The problem was posed for a fair (unbiased) coin tossing process by Prodinger [19] cf. also [10]) who provided the first non trivial analysis. Recently, for the same fair coin model, Fill et al. 5] find the limiting distribution for the number of rounds. In this paper, we analyze the same problem but when the coins involved are biased, that is, the probability p of throwing a head is not ....

....[18] for updated account on recent developments in this area. In fact, tries and other digital trees were used as a testbed for the precise analytical analysis of algorithms . Several new analytical techniques were developed in the process of analyzing different parameters of digital trees (cf. [4, 5, 10, 13, 14, 16, 20, 21, 22]) Recently, the focus of the research was moved towards developing analytical techniques that can handle limiting distributions and large deviations results (cf. 5, 11, 12, 14, 15] In this paper, we continue recent lines of research and establish asymptotic distribution together with the first ....

[Article contains additional citation context not shown here]

Grabner, P. Searching for losers. Random Structures and Algorithms, 4, 99--110, 1993.

....Grant CRG.950060. The second author also thanks INRIA, Sophia Antipolis, project MISTRAL for hospitality and support during the summer of 1996 when this paper was completed. the electronic journal of combinatorics 4 (1997) #R17 2 (unbiased) coin tossing process by Prodinger [19] cf. also [10]) who provided the first non trivial analysis. Recently, for the same fair coin model, Fill et al. 5] find the limiting distribution for the number of rounds. In this paper, we analyze the same problem but when the coins involved are biased, that is, the probability p of throwing a head is not ....

....[18] for updated account on recent developments in this area. In fact, tries and other digital trees were used as a testbed for the precise analytical analysis of algorithms . Several new analytical techniques were developed in the process of analyzing different parameters of digital trees (cf. [4, 5, 10, 13, 14, 16, 20, 21, 22]) Recently, the focus of the research was moved towards developing analytical techniques that can handle limiting distributions and large deviations results (cf. 5, 11, 12, 14, 15] In this paper, we continue recent lines of research and establish asymptotic distribution together with the first ....

[Article contains additional citation context not shown here]

Grabner, P. Searching for Losers. Random Structures and Algorithms, 4, 99--110, 1993.

....This time we denote the number of rounds by 1 RN;d . Observe that d = 0 corresponds to the original situation. Again we will expect RN;d to be an estimate of log 2 N . We should point out that a similar extension of the primary leader election algorithm was recently considered by Grabner [14]. Returning to the probabilistic counting algorithm: We can interpret the generalized situation as follows: We start from an empty bitmap string, that is, with all positions filled by zeros. We further assume that N different objects (e.g. data, persons, etc. can randomly insert (hit) a 1 at ....

P. Grabner, Searching for losers, Random Structures and Algorithms, 4, 99--110, 1993.

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Grabner, P. Searching for Losers. Random Structures and Algorithms , 4, 99--110, 1993.

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