Random Struct. Algorithms最新文献

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0-1 Laws for Maps 0-1地图法则

Random Struct. Algorithms

Pub Date : 1999-05-01 DOI: 10.1002/(SICI)1098-2418(199905)14:3%3C215::AID-RSA2%3E3.0.CO;2-K

E. Bender, K. Compton, L. Richmond

A class of finite structures has a 0–1 law with respect to a logic if every property expressible in the logic has a probability approaching a limit of 0 or 1 as the structure size grows. To formulate 0–1 laws for maps (i.e., embeddings of graphs in a surface), it is necessary to represent maps as logical structures. Three such representations are given, the most general being the full cross representation based on Tutte's theory of combinatorial maps. The main result says that if a class of maps has two properties, richness and large representativity, then the corresponding class of full cross representations has a 0–1 law with respect to first-order logic. As a corollary the following classes of maps on a surface of fixed type have a first-order 0–1 law: all maps, smooth maps, 2-connected maps, 3-connected maps, triangular maps, 2-connected triangular maps, and 3-connected triangular maps. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 14, 215–237, 1999

一类有限结构有一个0 - 1定律，如果逻辑中每个可表达的属性随着结构大小的增长有接近0或1极限的概率。要为地图(即在曲面上嵌入图形)制定0-1定律，有必要将地图表示为逻辑结构。给出了三种这样的表示，最一般的是基于Tutte的组合映射理论的全交叉表示。主要结果表明，如果一类映射具有两种性质，丰富性和大代表性，则相应的全交叉表示类具有关于一阶逻辑的0-1定律。作为一个推论，固定类型表面上的以下几类地图具有一阶0-1定律:所有地图、光滑地图、2连通地图、3连通地图、三角形地图、2连通三角形地图和3连通三角形地图。©1999 John Wiley & Sons, Inc随机结构。Alg。科学通报，14,215-237,1999

引用次数: 8

On the variance of the random sphere of influence graph 论随机影响球图的方差

Random Struct. Algorithms

Pub Date : 1999-03-01 DOI: 10.1002/(SICI)1098-2418(199903)14:2%3C139::AID-RSA2%3E3.0.CO;2-E

P. Hitczenko, S. Janson, J. Yukich

We show that the variance of the number of edges in the random sphere of influence graph built on n i.i sites which are uniformly distributed over the unit cube in R-d, grows linearly with n. This is then used to establish a central limit theorem for the

我们证明了在R-d中均匀分布在单位立方体上的n. i.i个点上建立的随机影响球图的边数的方差随n线性增长。这随后被用于建立的中心极限定理

引用次数: 10

On the multiplicity of parts in a random partition 关于随机分区中部分的多重性

Random Struct. Algorithms

Pub Date : 1999-03-01 DOI: 10.1002/(SICI)1098-2418(199903)14:2%3C185::AID-RSA4%3E3.0.CO;2-F

S. Corteel, B. Pittel, C. Savage, H. Wilf

Let λ be a partition of an integer n chosen uniformly at random among all such partitions. Let s(λ) be a part size chosen uniformly at random from the set of all part sizes that occur in λ. We prove that, for every fixed m≥1, the probability that s(λ) has multiplicity m in λ approaches 1/(m(m+1)) as n∞. Thus, for example, the limiting probability that a random part size in a random partition is unrepeated is 1/2. In addition, (a) for the average number of different part sizes, we refine an asymptotic estimate given by Wilf, (b) we derive an asymptotic estimate of the average number of parts of given multiplicity m, and (c) we show that the expected multiplicity of a randomly chosen part size of a random partition of n is asymptotic to (log n)/2. The proofs of the main result and of (c) use a conditioning device of Fristedt. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 14, 185–197, 1999

设λ是一个整数n的分区，在所有这样的分区中均匀随机选择。设s(λ)为从λ中出现的所有零件尺寸集合中均匀随机选择的零件尺寸。我们证明了，对于每一个固定的m≥1,s(λ)在λ趋于1/(m(m+1))时有多重数m的概率为n∞。因此，例如，随机分区中随机零件尺寸不重复的极限概率为1/2。此外，(a)对于不同零件尺寸的平均数量，我们改进了Wilf给出的渐近估计，(b)我们导出了给定多重度m的零件平均数量的渐近估计，(c)我们证明了n的随机分区的随机选择零件尺寸的期望多重度渐近于(log n)/2。主要结果和(c)的证明使用了弗里斯泰特的调节装置。©1999 John Wiley & Sons, Inc随机结构。Alg。中文信息学报，14,185-197,1999

引用次数: 49

Techniques for bounding the convergence rate of genetic algorithms 约束遗传算法收敛速度的技术

Random Struct. Algorithms

Pub Date : 1999-03-01 DOI: 10.1002/(SICI)1098-2418(199903)14:2%3C111::AID-RSA1%3E3.0.CO;2-6

Y. Rabinovich, A. Wigderson

The main purpose of the present paper is the study of computational aspects, and primarily the convergence rate, of genetic algorithms (GAs). Despite the fact that such algorithms are widely used in practice, little is known so far about their theoretical properties, and in particular about their long-term behavior. This situation is perhaps not too surprising, given the inherent hardness of analyzing nonlinear dynamical systems, and the complexity of the problems to which GAs are usually applied. In the present paper we concentrate on a number of very simple and natural systems of this sort, and show that at least for these systems the analysis can be properly carried out. Various properties and tight quantitative bounds on the long-term behavior of such systems are established. It is our hope that the techniques developed for analyzing these simple systems prove to be applicable to a wider range of genetic algorithms, and contribute to the development of the mathematical foundations of this promising optimization method. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 14, 111–138, 1999

本文的主要目的是研究遗传算法的计算方面，主要是收敛速度。尽管这样的算法在实践中被广泛使用，但迄今为止对它们的理论性质，特别是它们的长期行为知之甚少。考虑到分析非线性动力系统固有的困难，以及通常应用GAs的问题的复杂性，这种情况可能并不太令人惊讶。在本文中，我们集中讨论了这类非常简单和自然的系统，并表明至少对于这些系统，可以适当地进行分析。建立了这类系统长期行为的各种性质和严格的定量界限。我们希望，用于分析这些简单系统的技术被证明适用于更广泛的遗传算法，并有助于发展这种有前途的优化方法的数学基础。©1999 John Wiley & Sons, Inc随机结构。Alg。科学通报，14,111-138,1999

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引用次数: 31

Finding a large hidden clique in a random graph 在随机图中找到一个隐藏的大集团

Random Struct. Algorithms

Pub Date : 1998-10-01 DOI: 10.1002/(SICI)1098-2418(199810/12)13:3/4%3C457::AID-RSA14%3E3.0.CO;2-W

N. Alon, M. Krivelevich, B. Sudakov

We consider the following probabilistic model of a graph on n labeled vertices. . First choose a random graph Gn ,1 r 2 ,and then choose randomly a subset Q of vertices of size k and force it to be a clique by joining every pair of vertices of Q by an edge. The problem is to give a polynomial time algorithm for finding this hidden clique almost surely for various values of k. This question was posed independently, in various variants, by Jerrum and by Kucera. In this paper we present an efficient algorithm for all k ) cn 0.5 , for ˇ 0.5 . 0.5 any fixed c ) 0, thus improving the trivial case k ) cn log n . The algorithm is based on the spectral properties of the graph. Q 1998 John Wiley & Sons, Inc. Random Struct. Alg., 13, 457)466, 1998

我们考虑有n个标记顶点的图的以下概率模型。首先选择一个随机图Gn,1 r 2，然后随机选择大小为k的顶点的子集Q，并通过将Q的每个顶点对通过一条边连接来强制它成为一个团。问题是给出一个多项式时间算法，几乎可以确定地找到这个隐藏的团对于不同的k值。这个问题是由Jerrum和kuucera以不同的变体独立提出的。在本文中，我们提出了一种有效的算法，适用于所有k) cn 0.5，适用于loc0.5。0.5任意固定的c) 0，从而改进了平凡的情况k) cn log n。该算法基于图的谱特性。John Wiley & Sons, Inc.;随机结构。Alg。[中文]，13,457)466,1998

引用次数: 422

The number of Boolean functions computed by formulas of a given size 由给定大小的公式计算的布尔函数的数目

Random Struct. Algorithms

Pub Date : 1998-10-01 DOI: 10.1002/(SICI)1098-2418(199810/12)13:3/4%3C349::AID-RSA9%3E3.0.CO;2-V

P. Savický, Alan R. Woods

Estimates are given of the number B(n, L) of distinct functions computed by propositional formulas of size L in n variables, constructed using only literals and ∧, ∨ connectives. (L is the number of occurrences of variables. L−1 is the number of binary ∧s and ∨s. B(n, L) is also the number of functions computed by two terminal series-parallel networks with L switches.) Enroute the read-once functions, which are closely related to Schroder numbers, are enumerated. Writing B(n, L)=b(n, L)L, we find that if L and β(n) go to infinity with increasing n and L≤2n/nβ(n), then b(n, L)∼cn, where c=2/(ln 4−1). Making a comparison with polynomial size Boolean circuits, this implies the following. For any constant α>1, almost all Boolean functions with formula complexity at most nα cannot be computed by any circuit constructed from literals and fewer than α−1nα two-input ∧, ∨ gates. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 13: 349–382, 1998

给出由大小为L的命题公式在n个变量中计算的不同函数的个数B(n, L)的估计，这些函数只使用字面量和∧，∨连接词构造。(L是变量出现的次数。L−1是二元∧s和对偶的个数。B(n, L)也是两个终端串并联网络(L交换机)计算的函数数。在此过程中，将枚举与Schroder数密切相关的一次性读取函数。令B(n, L)= B(n, L)L，我们发现如果L和β(n)随n的增大而趋于无穷，且L≤2n/nβ(n)，则B(n, L) ~ cn，其中c=2/(ln 4−1)。与多项式大小的布尔电路进行比较，这意味着以下几点。对于任意常数α>1，几乎所有公式复杂度不超过nα的布尔函数都不能由小于α−1nα双输入∧门构造的任何电路来计算。©1998 John Wiley & Sons, Inc随机结构。Alg。中文信息学报，13:349-382,1998

引用次数: 29

On the joint distribution of the nodes in uniform multidimensional binary trees 一致多维二叉树中节点的联合分布

Random Struct. Algorithms

Pub Date : 1998-10-01 DOI: 10.1002/(SICI)1098-2418(199810/12)13:3/4%3C261::AID-RSA5%3E3.0.CO;2-T

R. Kemp

Multidimensional binary trees represent a symbiosis of trees and tries, and they essentially arise in the construction of search trees for multidimensional keys. The set of nodes in a d-dimensional binary tree can be partitioned into layers according to the nodes appearing in the ith dimension. We determine the exact distribution of the number of nodes with zero, one, and two sons in a specified layer and show that jointly the three types of nodes asymptotically have a trivariate normal distribution in each layer. That trivariate normal distribution is completely characterized. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 13: 261–283, 1998

引用次数: 4

Partial Steiner systems and matchings in hypergraphs 超图中的部分斯坦纳系统与匹配

Random Struct. Algorithms

Pub Date : 1998-10-01 DOI: 10.1002/(SICI)1098-2418(199810/12)13:3/4%3C335::AID-RSA8%3E3.0.CO;2-W

A. Kostochka, V. Rödl

引用次数: 24

Predecessors in a random mapping 随机映射中的前辈

Random Struct. Algorithms

Pub Date : 1998-10-01 DOI: 10.1002/(SICI)1098-2418(199810/12)13:3/4%3C501::AID-RSA17%3E3.0.CO;2-0

J. Jaworski

Ž . 4 ABSTRACT: A random mapping T ; q of a finite set V, Vs 1, 2, . . . , n into itself assigns independently to each igV its unique image jgV with probability q if is j and with Ž . Ž . probability Ps 1yq r ny1 if i/ j. The number of predecessors of elements from a given subset of V is studied. Exact results and limit theorems for the distribution of this random variable, the quasi-binomial distribution, are given. The results are applied to an Ž . inverse epidemic process on a random digraph G representing T ; q . Q 1998 John Wiley & T Sons, Inc. Random Struct. Alg., 13, 501]519, 1998

Ž。摘要:随机映射T;有限集合V, V 1,2，…的q。， n into自身独立地为每个igV分配其唯一的图像jgV，其概率为q，如果为j，则为Ž。Ž。如果i/ j，则概率为p 1yq r ny1。研究了给定V子集中元素的前导个数。给出了拟二项分布的精确结果和极限定理。结果应用于Ž。表示T的随机有向图G上的逆流行过程;q。1998 John Wiley & T Sons, Inc.;随机结构。Alg。[j] .农业科学，1998,18 (2):1 - 5

引用次数: 18

On the asymptotic distributions of subgraph counts in a random tournament 随机竞赛中子图计数的渐近分布

Random Struct. Algorithms

Pub Date : 1998-10-01 DOI: 10.1002/(SICI)1098-2418(199810/12)13:3/4%3C249::AID-RSA4%3E3.0.CO;2-V

Pontus Andersson

A random tournament T-n is obtained by independently orienting the edges of the complete graph on n vertices, with probability 1/2 far each direction. We study the asymptotic distribution, as n ten ...

随机竞赛T-n是通过在n个顶点上独立定向完整图的边来获得的，每个方向的概率为1/2。我们研究渐近分布，如n 10…

引用次数: 2

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