V.F. Kolchin, B.A. Senast'yanov, and V.P. Chistyakov. Random Allocation. V.H. Winston & Sons, Washington D.C. 1978.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....fact that H 2,i has some correlation with H 2,i a and H 2,i a . This will be taken into account in Sec. 3.4. 7 3.3 # = 1 2 As p 2 1 n, we see that we are in the realm of asymptotic Poisson distribution, with mean 1. This can be checked by the method of moments (see, for instance, Kolchin et al. [10], Barbour et al. 2] First, by Poissonization dePoissonization as exposed in the nice paper by Jacquet and Szpankowski, 8] we can again consider all urns as independent. We obtain M 2 = n a)p 2 (3n # 1 n # 2 )p 4 (n # 3 n # 4 n # 5 )p 6 (6n # 7 )p 3 (6n ....

V.K. Kolchin, A.S. Sevastyanov, and P.C. Chistiakov. Random Allocations. Wiley, 1978.

....K max N , throw each object with index k into box number k mod N . The number of boxes required in this case is N. 2. If K max N , throw each object with index k into box number k mod K max . The number of boxes required in this case is K max . 11 The probability P (K max = l) is derived in [8, 17] and is given by: P (K max l) 6 4e l b=0 b b 7 (4) P (K max = l) P (K max l) P (K max l 1) for 1 l K (5) The average data cycle length (or the average minimum number of boxes) is given by: LLM (M;K;C) NP (K max N) l=N 1 lP (K max = l) where N = ....

KOLCHIN, V. F., SEVASTYANOV, B. A., AND CHISTYAKOV, V. P. Random Allocations. John Wiley and Sons, New York, 1978. Translated from the Russian original Slu cajnye Razmes ceniya.

....N , throw each object with index k into cell number given by k mod N . The number of cells required in this case is N. If Kmax N , throw each object with index k into cell number given by k mod Kmax . The number of cells required in this case is Kmax . The probability P (Kmax = l) is derived in [21, 22] and is given by: P (Kmax l) # M (1) P (Kmax = l) P (Kmax l) Gamma P (Kmax l Gamma 1) 2) 3) where 1 l K . The average data cycle length (L) or the average minimum number of cells) and utilization (G) for LiteMAC and FatMAC and is given by: LLM = NP (Kmax N) l=N 1 ....

V. F. Kolchin, B. A. Sevastyanov, and V. P. Chistyakov, Random Allocations. New York: John Wiley and Sons, 1978. Translated from the Russian original Slucajnye Razmesceniya.

....for tag messages is called frame size and will be denoted by . The number of tags is usually denoted by . 3. 1 Occupancy Problems The allocation of tags to slots within a time frame belongs to a class of problems that are known as occupancy problems, which are well studied in the literature [4, 5] and widely applied [8, 9] These problems deal with the random allocation of balls to a number of bins where one is, e.g. interested in the number of filled bins. In the following, we will speak of tags and slots instead of balls and bins . Given slots and tags, the number of ....

Valentin F. Kolchin, Boris A. Svast'yanov, and Valdimir P. Christyakov. Random Allocations. V. H. Winston & Sons, 1978.

....analysis, we are not interested in the actual data sent by the tags, but only in the quantities of empty, filled, and (due to collisions) garbled slots. Such a read result will be represented by the triple . The allocation of tags to slots belongs to the class of occupancy problems [3] [4]. Given N slots and n tags, the number r of tags in one slot is binomially distributed, and the expectation value for the number of slots that all have r tags assigned to them is given by the occupancy number a r : a r = N n r . 1) Maximum throughput is reached when the number of slots ....

Valentin F. Kolchin, Boris A. Svast'yanov, and Vladimir P. Christyakov. Random Allocations. V. H. Winston & Sons, 1978.

....frame available for tag messages is called frame size and will be denoted by N. The number of tags is usually denoted by n. 3. 1 Occupancy Problems The allocation of tags to slots within a time frame belongs to a class of problems that are known as occupancy problems, which are well studied [5, 4] and widely applied [8, 9] These problems deal with the allocation of balls to a number of bins where one is, e.g. interested in the number of filled bins. In the following, we will speak of tags and slots instead of balls and bins . Given N slots and n tags, the number r of tags in one ....

Valentin F. Kolchin, Boris A. Svast'yanov, and Valdimir P. Christyakov. Random Allocations. V. H. Winston & Sons, 1978.

....bin and where D = L Gamma N=M. 1.2 Related work Let us compare our results for the random arc allocation to the well known results for balls into bins processes. These processes are among of the most intensively studied stochastic processes in the context of algorithm analysis (e.g. [14, 22, 16, 12, 2, 23, 15, 19, 4]) The simplest balls into bins process assumes that N balls are placed i.u.r. into M bins [14, 22, 16] Balls into bins are the special case of chains into bins where all chains consist of a single ball, i.e. n = N. We get M ln M r logM if N =W(M logM) 6) The Bounds (5) and ....

....well known results for balls into bins processes. These processes are among of the most intensively studied stochastic processes in the context of algorithm analysis (e.g. 14, 22, 16, 12, 2, 23, 15, 19, 4] The simplest balls into bins process assumes that N balls are placed i.u.r. into M bins [14, 22, 16]. Balls into bins are the special case of chains into bins where all chains consist of a single ball, i.e. n = N. We get M ln M r logM if N =W(M logM) 6) The Bounds (5) and (6) are well known although other papers [14, 22, 16] use a different, slightly more complicated ....

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V. F. Kolchin, B. A. Sevatyanov, and V. P. Chistiakov. Random Allocations. V. H. Winston, 1978.

....illustrate. Returning to our balls and bins, let c 1 1 in (11) say c 1 = 2. Now, Pr[X (1 ffi) Pr[ j2[n] X j (1 ffi) X j2[n] Pr[X j (1 ffi) union bound) n Delta n Gammac 1 (by (11) n 1 Gammac 1 ; which is quite small for c 1 1. The reader is referred to [41, 30, 19] for other such useful results about this and related processes. 3.2 Approximation algorithms for job shop scheduling We now show a more involved application of the above approach to job shop scheduling, which is a classical NP hard minimization problem [44] In it, we have n jobs and m ....

V. F. Kolchin, B. A. Sevastyanov, and V. P. Chistyakov. Random Allocations. John Wiley & Sons, 1978. 49

....models that have been proposed to study the dynamical behaviour of relational databases. The second author introduced urn models to study the so called sizes of relations obtained by projection or joins [8, 9] The projection model is basically a generalization of the empty urns model (see [15] for a detailed presentation of this last model, both for the asymptotic distribution and for the limiting process under a large set of assumptions) and we gave in [6] an analysis of the asymptotic process in a restricted dynamic case (balls are added one at a time, no deletions are allowed) The ....

V. F. Kolchin, B. Sevast'yanov, and V. Chistyakov, Random Allocations, Wiley, New York, 1978.

....60G99, 60G10, 90C40 PII. S0097539795288490 1. Introduction. Suppose that we sequentially place n balls into n boxes by putting each ball into a randomly chosen box. Properties of this random allocation process have been extensively studied in the probability and statistics literature. See, e.g. [20, 17]. One of the classical results in this area is that, asymptotically, when the process has terminated, with high probability (that is, with probability 1 o(1) the fullest box contains (1 o(1) ln n ln ln n balls. G. Gonnet [16] has proven a more accurate result, # 1 (n) 3 2 o(1) ....

V. F. Kolchin, B. A. Sevastyanov, and V. P. Chistyakov, Random Allocations, John Wiley & Sons, New York, 1978.

.... have established only for fixed h) shows that this probability is asymptotically distributed like a Poisson random variable with parameter n exp( m n) Many additional results on random distributions of balls into cells, and references to the extensive literature on this subject can be found in [241]. Xi Bonferroni inequalities include other methods for estimating N= R) by linear combinations of the N# (Q) Recent approaches and references (phrased in probabilistic terms) can be found in [152] For bivariate Bonferroni inequalities (where one asks for the probability that at least one of ....

....this chapter has been on elementary and generating function approaches to asymptotic enumeration problems. Probabilistic methods provide another way to approach many of 155 these problems. This has been appreciated more in the former Soviet Union than in the West, as can be seen in the books [240, 241, 338]. The last few years have seen a great increase in the applications of probabilistic methods to combinatorial enumeration and analysis of algorithms. Many powerful tools, such as martingales, branching processes, and Brownian motion asymptotics have been brought to bear on this topic. General ....

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V. F. Kolchin, B. A. Sevast'yanov, and V. P. Chistyakov, Random Allocations, Wiley, 1978.

....capacit e infinie. 1 Les r ef erences de base ffl N.L. JOHNSON and S. KOTZ, Urn models and their application. 25] Le livre de base sur tous les problemes d urnes; r ef erence tr es g en erale, mais un peu ancienne. ffl V. KOLCHIN and B. SEVAST YANOV and V. CHISTYAKOV, Random Allocations , [29] Etudie plus particuli erement le nombre d urnes vides, ou avec k boules; lois limites; methode de col; etudes dynamiques. ffl V.N. SACHKOV, Probabilistic methods in combinatorial analysis , 39] Ne traite pas sp ecialement des probl emes d urnes; plus dans l optique de combinatoire ....

V. KOLCHIN, B. SEVAST'YANOV, and V. CHISTYAKOV. Random Allocations. Wiley & Sons, 1978.

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V.F. Kolchin, B.A. Senast'yanov, and V.P. Chistyakov. Random Allocation. V.H. Winston & Sons, Washington D.C. 1978.

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V. Kolchin, B. Sevastyanov, and V. Chistyakov, Random Allocations. Wiley, 1978.

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V.F. Kolchin, B.A. Sevastyanov, and V.P. Chistyakov, Random allocations, John Wiley & Sons, 1978.

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V.K. Kolchin, A.S. Sevastyanov, and P.C. Chistiakov. Random Allocations. Wiley, 1978.

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V. F. Kolchin, B. Sevast'yanov, and V. Chistyakov, Random allocations, Wiley, New York, 1978.

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V.K. Kolchin, A.S. Sevastyanov, and P.C. Chistiakov. Random Allocations. Wiley, 1978.

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V.F.Kolchin, B.A.Sevastyanov, and V.P.Chistaykov, Random Allocations, Winston, 1978.

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V. F. Kolchin, B. Sevast'yanov, and V. Chistyakov, Random allocations, Wiley, New York, 1978.

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V.F.Kolchin, B.A.Sevastyanov, and V.P.Chistaykov, Random Allocations, Winston, 1978.

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V. F. Kolchin, B. Sevast'yanov, and V. Chistyakov. Random Allocations. Wiley, New-York, 1978.

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V.F. Kolchin, B.A. Sevastyanov, and V.P. Chistyakov, Random allocations, John Wiley & Sons, 1978.

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V. F. Kolchin, B. A. Sevsat'yanov, and V. P. Chistyakov. Random Allocations.V.H. Winston & Sons, 1978.

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V. F. Kolchin, B. A. Sevsat'yanov, and V. P. Chistyakov. Random Allocations. V. H. Winston & Sons, 1978.

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