Random Struct. Algorithms最新文献

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A Poisson * Negative Binomial Convolution Law for Random Polynomials over Finite Fields 有限域上随机多项式的Poisson *负二项式卷积律

Random Struct. Algorithms

Pub Date : 1998-08-01 DOI: 10.1002/(SICI)1098-2418(199808)13:1%3C17::AID-RSA2%3E3.0.CO;2-V

Hsien-Kuei Hwang

Let Fq[X] denote a polynomial ring over a finite field Fq with q elements. Let n be the set of monic polynomials over Fq of degree n. Assuming that each of the qn possible monic polynomials in n is equally likely, we give a complete characterization of the limiting behavior of P(Ωn=m) as n∞ by a uniform asymptotic formula valid for m≥1 and n−m∞, where Ωn represents the number (multiplicities counted) of irreducible factors in the factorization of a random polynomial in n. The distribution of Ωn is essentially the convolution of a Poisson distribution with mean log n and a negative binomial distribution with parameters q and q−1. Such a convolution law exhibits three modes of asymptotic behaviors: when m is small, it behaves like a Poisson distribution; when m becomes large, its behavior is dominated by a negative binomial distribution, the transitional behavior being essentially a parabolic cylinder function (or some linear combinations of the standard normal law and its iterated integrals). As applications of this uniform asymptotic formula, we derive most known results concerning P(Ωn=m) and present many new ones like the unimodality of the distribution. The methods used are widely applicable to other problems on multiset constructions. An extension to Renyi's problem, concerning the distribution of the difference of the (total) number of irreducibles and the number of distinct irreducibles, is also presented. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 13, 17–47, 1998

设Fq[X]表示有限域Fq上有q个元素的多项式环。设n为Fq上n次的一元多项式的集合。假设n中qn个可能的一元多项式中的每一个都是等可能的，我们用一个对m≥1和n−m∞有效的一致渐近公式给出了P(Ωn=m)在n∞时的极限行为的完整表征。其中Ωn表示在n中随机多项式的分解中不可约因子的数量(计数的多重性)。Ωn的分布本质上是均值为log n的泊松分布和参数为q和q−1的负二项分布的卷积。这样的卷积律表现出三种渐近行为模式:当m很小时，它表现为泊松分布;当m变大时，其行为由负二项分布主导，过渡行为本质上是抛物线柱面函数(或标准正态律及其迭代积分的一些线性组合)。作为这个一致渐近公式的应用，我们得到了关于P(Ωn=m)的大多数已知结果，并提出了许多新的结果，如分布的单模性。所采用的方法可广泛应用于其他多集结构问题。本文还对Renyi的问题作了推广，讨论了不可约物总数与不同不可约物总数之差的分布。©1998 John Wiley & Sons, Inc随机结构。Alg。， 13, 17-47, 1998

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引用次数: 4

Variable orderings and the size of OBDDs for random partially symmetric Boolean functions 随机部分对称布尔函数的可变顺序和obdd的大小

Random Struct. Algorithms

Pub Date : 1998-08-01 DOI: 10.1002/(SICI)1098-2418(199808)13:1%3C49::AID-RSA3%3E3.0.CO;2-S

Detlef Sieling

The size of ordered binary decision diagrams (OBDDs) strongly depends on the chosen variable ordering. It is an obvious heuristic to use symmetric variable orderings, i.e., variable orderings where symmetric variables are arranged adjacently. In order to evaluate this heuristic, methods for estimating the OBDD size for random partially symmetric functions are presented. Characterizations of cases where, with high probability, only symmetric variable orderings and, with high probability, only nonsymmetric variable orderings lead to minimum OBDD size are obtained. For this analysis estimates for the number of different blocks of random Boolean matrices are used. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 13, 49–70, 1998

有序二元决策图(obdd)的大小很大程度上取决于所选择的变量排序。使用对称变量排序是一个明显的启发式方法，即对称变量相邻排列的变量排序。为了评估这种启发式，给出了估计随机部分对称函数的OBDD大小的方法。给出了高概率下只有对称变量排序和高概率下只有非对称变量排序导致最小OBDD大小的情况的特征。对于这种分析，估计了随机布尔矩阵的不同块的数量。©1998 John Wiley & Sons, Inc随机结构。Alg。， 13, 49-70, 1998

引用次数: 11

Recursive reconstruction on periodic trees 周期树上的递归重构

Random Struct. Algorithms

Pub Date : 1998-08-01 DOI: 10.1002/(SICI)1098-2418(199808)13:1%3C81::AID-RSA5%3E3.0.CO;2-O

Elchanan Mossel

A periodic tree Tn consists of full n-level copies of a finite tree T. The tree Tn is labeled by random bits. The root label is chosen randomly, and the probability of two adjacent vertices to have the same label is 1−ϵ. This model simulates noisy propagation of a bit from the root, and has significance both in communication theory and in biology. Our aim is to find an algorithm which decides for every set of values of the boundary bits of T, if the root is more probable to be 0 or 1. We want to use this algorithm recursively to reconstruct the value of the root of Tn with a probability bounded away from ½ for all n. In this paper we find for all T, the values of ϵ for which such a reconstruction is possible. We then compare the ϵ values for recursive and nonrecursive algorithms. Finally, we discuss some problems concerning generalizations of this model. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 13, 81–97, 1998

周期树Tn由有限树t的完整n层副本组成，树Tn用随机位标记。根标签是随机选择的，两个相邻顶点具有相同标签的概率为1−λ。该模型模拟了比特从根开始的噪声传播，在通信理论和生物学上都有重要意义。我们的目标是找到一种算法来决定T的每一组边界位的值，如果根更有可能是0或1。我们想用这个算法递归地重建Tn的根的值，对于所有的n，概率有界于1 / 2。在本文中，我们发现对于所有的T，这样的重建是可能的。然后我们比较递归和非递归算法的λ值。最后，我们讨论了关于该模型推广的一些问题。©1998 John Wiley & Sons, Inc随机结构。Alg。， 13, 81-97, 1998

引用次数: 47

The chromatic numbers of random hypergraphs 随机超图的色数

Random Struct. Algorithms

Pub Date : 1998-07-01 DOI: 10.1002/(SICI)1098-2418(199807)12:4%3C381::AID-RSA5%3E3.0.CO;2-P

M. Krivelevich, B. Sudakov

For a pair of integers 1 < r, the -chromatic number of an r-uniform hypergraph H = (V;E) is the minimal k, for which there exists a partition of V into subsets T1; : : : ; Tk such that jeTij for every e 2 E. In this paper we determine the asymptotic behavior of the -chromatic number of the random r-uniform hypergraph Hr(n; p) for all possible values of and for all values of p down to p = (n r+1).

对于整数对1 < r，一个r-一致超图H = (V;E)的-色数是最小k，对于这个超图，存在V划分为子集T1;:::;在本文中，我们确定了随机r-均匀超图Hr(n;P的所有可能值和P的所有值直到P = (n r+1)

引用次数: 47

On the log-product of the subtree-sizes of random trees 关于随机树的子树大小的对数积

Random Struct. Algorithms

Pub Date : 1998-07-01 DOI: 10.1002/(SICI)1098-2418(199803)12:2%3C197::AID-RSA3%3E3.0.CO;2-S

A. Meir, J. Moon

引用次数: 5

An elementary analysis of a procedure for sampling points in a convex body 对凸体中采样点程序的初步分析

Random Struct. Algorithms

Pub Date : 1998-05-01 DOI: 10.1002/(SICI)1098-2418(199805)12:3%3C213::AID-RSA1%3E3.0.CO;2-Y

Russ Bubley, M. Dyer, M. Jerrum

In this paper we describe a new method for proving the polynomial-time convergence of an algorithm for sampling (almost) uniformly at random from a convex body in high dimension. Previous approaches have been based on estimating conductance via isoperimetric inequalities. We show that a more elementary coupling argument can be used to give a similar result. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 12, 213–235, 1998

引用次数: 19

Tree decomposition of graphs 图的树分解

Random Struct. Algorithms

Pub Date : 1998-05-01 DOI: 10.1002/(SICI)1098-2418(199805)12:3%3C237::AID-RSA2%3E3.0.CO;2-W

R. Yuster

Let H be a tree on h≥2 vertices. It is shown that if G=(V, E) is a graph with delta (G)ge (|V|/2)+10h^4sqrt{|V|log|V|}, and h−1 divides |E|, then there is a decomposition of the edges of G into copies of H. This result is asymptotically the best possible for all trees with at least three vertices. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 12, 237–251, 1998

引用次数: 14

A study of random Weyl trees 随机Weyl树的研究

Random Struct. Algorithms

Pub Date : 1998-05-01 DOI: 10.1002/(SICI)1098-2418(199805)12:3%3C271::AID-RSA4%3E3.0.CO;2-S

L. Devroye, Amar Goudjil

We study binary search trees constructed from Weyl sequences fnng; n 1, where is an irrational and f:g denotes mod 1". We explore various properties of the structure of these trees, and relate them to the continued fraction expansion of. If H n is the height of the tree with n nodes when is chosen at random and uniformly on 0; 1], then we show that in probability, H n (12== 2) log n log log n.

研究了基于Weyl序列的二叉搜索树;N 1，其中是无理数，f:g表示mod 1 '。我们探索了这些树结构的各种性质，并将它们与的连分式展开联系起来。设H n为n节点树的高度，在0上随机均匀选择;1]，然后我们证明在概率中，H n (12== 2) log n log n。

引用次数: 5

Approximating the unsatisfiability threshold of random formulas 随机公式不满意阈值的逼近

Random Struct. Algorithms

Pub Date : 1998-05-01 DOI: 10.1002/(SICI)1098-2418(199805)12:3%3C253::AID-RSA3%3E3.0.CO;2-U

L. Kirousis, E. Kranakis, D. Krizanc, Y. Stamatiou

Let f be a random Boolean formula that is an instance of 3-SAT. We consider the problem of computing the least real number k such that if the ratio of the number of clauses over the number of variables of f strictly exceeds k , then f is almost certainly unsatisfiable. By a well-known and more or less straightforward argument, it can be shown that kF5.191. This upper bound was improved by Kamath et al. to 4.758 by first providing new improved bounds for the occupancy problem. There is strong experimental evidence that the value of k is around 4.2. In this work, we define, in terms of the random formula f, a decreasing sequence of random variables such that, if the expected value of any one of them converges to zero, then f is almost certainly unsatisfiable. By letting the expected value of the first term of the sequence converge to zero, we obtain, by simple and elementary computations, an upper bound for k equal to 4.667. From the expected value of the second term of the sequence, we get the value 4.601q . In general, by letting the U This work was performed while the first author was visiting the School of Computer Science, Carleton Ž University, and was partially supported by NSERC Natural Sciences and Engineering Research Council . of Canada , and by a grant from the University of Patras for sabbatical leaves. The second and third Ž authors were supported in part by grants from NSERC Natural Sciences and Engineering Research . Council of Canada . During the last stages of this research, the first and last authors were also partially Ž . supported by EU ESPRIT Long-Term Research Project ALCOM-IT Project No. 20244 . †An extended abstract of this paper was published in the Proceedings of the Fourth Annual European Ž Symposium on Algorithms, ESA’96, September 25]27, 1996, Barcelona, Spain Springer-Verlag, LNCS, . pp. 27]38 . That extended abstract was coauthored by the first three authors of the present paper. Correspondence to: L. M. Kirousis Q 1998 John Wiley & Sons, Inc. CCC 1042-9832r98r030253-17 253

设f是一个随机布尔公式，它是3-SAT的一个实例。我们考虑计算最小实数k的问题，如果子句数与f的变量数之比严格超过k，则f几乎肯定是不满足的。通过一个众所周知的或多或少直截了当的论证，可以证明kF5.191。Kamath等人首先为占用问题提供了新的改进边界，将该上界改进为4.758。有强有力的实验证据表明，k的值在4.2左右。在这项工作中，我们根据随机公式f定义了一个递减的随机变量序列，如果其中任何一个的期望值收敛于零，那么f几乎肯定是不满足的。通过让序列第一项的期望值收敛于零，通过简单的初等计算，我们得到k的上界等于4.667。从序列第二项的期望值，我们得到值4.601q。这项工作是在第一作者访问卡尔顿Ž大学计算机科学学院期间进行的，并得到了NSERC自然科学与工程研究委员会的部分支持。由加拿大帕特雷大学(University of Patras)授予的公休假。第二和第三位Ž作者得到了NSERC自然科学与工程研究的部分资助。加拿大理事会。在这项研究的最后阶段，第一和最后的作者也部分Ž。欧盟ESPRIT长期研究项目ALCOM-IT项目(20244)资助。†本文的扩展摘要发表在第四届欧洲年会论文集Ž算法研讨会，ESA ' 96, September 25]27, 1996，巴塞罗那，西班牙。[27]该扩展摘要是由本文的前三位作者共同撰写的。致:l.m. Kirousis Q 1998 John Wiley & Sons, Inc。CCC 1042-9832r98r030253-17

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引用次数: 201

Emergence of the giant component in special Marcus-Lushnikov processes 特殊Marcus-Lushnikov过程中巨分量的出现

Random Struct. Algorithms

Pub Date : 1998-03-01 DOI: 10.1002/(SICI)1098-2418(199803)12:2%3C179::AID-RSA2%3E3.0.CO;2-U

D. Aldous

Author(s): Aldous, D | Abstract: Component sizes in the usual random graph process are a special case of the Marcus-Lushnikov process discussed in the scientific literature, so it is natural to ask how theory surrounding emergence of the giant component generalizes to the Marcus-Lushnikov process. Essentially no rigorous results are known; we make a start by proving a weak result, but our main purpose is to draw this topic to the attention of random graph theorists. © 1998 John Wiley a Sons, Inc. Random Struct. Alg., 12, 179-196, 1998.

摘要:通常随机图过程中的分量大小是科学文献中讨论的Marcus-Lushnikov过程的一个特例，因此人们很自然地要问，围绕巨大分量出现的理论如何推广到Marcus-Lushnikov过程。基本上没有确切的结果;我们从证明一个弱结果开始，但我们的主要目的是提请随机图理论家注意这个主题。©1998 John Wiley a Sons, Inc随机结构。Alg。中文信息学报，12,179-196,1998。

引用次数: 25

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