Random Struct. Algorithms最新文献

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Fast convergence of the Glauber dynamics for sampling independent sets 采样独立集的Glauber动态的快速收敛

Random Struct. Algorithms

Pub Date : 1999-10-01 DOI: 10.1002/(SICI)1098-2418(199910/12)15:3/4%3C229::AID-RSA3%3E3.0.CO;2-X

M. Luby, Eric Vigoda

We consider the problem of sampling independent sets of a graph with maximum degree δ. The weight of each independent set is expressed in terms of a fixed positive parameter λ≤2/(δ−2), where the weight of an independent set σ is λ|σ|. The Glauber dynamics is a simple Markov chain Monte Carlo method for sampling from this distribution. We show fast convergence (in O(n log n) time) of this dynamics. This paper gives the more interesting proof for triangle-free graphs. The proof for arbitrary graphs is given in a companion paper (E. Vigoda, Technical Report TR-99-003, International Computer Institute, Berkeley, CA, 1998). We also prove complementary hardness of approximation results, which show that it is hard to sample from this distribution when λ>c/δ for a constant c≤0. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 15, 229–241, 1999

考虑最大度为δ的图的抽样独立集问题。每个独立集的权值用一个固定的正参数λ≤2/(δ−2)表示，其中独立集的权值σ为λ|σ|。格劳伯动力学是一种简单的马尔可夫链蒙特卡罗方法，用于从该分布中采样。我们展示了这种动态的快速收敛(在O(n log n)时间内)。本文给出了一个更有趣的无三角形图的证明。任意图的证明在一篇配套论文中给出(E. Vigoda, Technical Report TR-99-003, International Computer Institute, Berkeley, CA, 1998)。我们还证明了近似结果的互补硬度，这表明当常数c≤0时λ>c/δ很难从该分布中采样。©1999 John Wiley & Sons, Inc随机结构。Alg。科学通报，15,229-241,1999

引用次数: 104

On near-critical and dynamical percolation in the tree case 树状情况下的近临界和动态渗流

Random Struct. Algorithms

Pub Date : 1999-10-01 DOI: 10.1002/(SICI)1098-2418(199910/12)15:3/4%3C311::AID-RSA7%3E3.0.CO;2-6

Olle Häggström, Robin Pemantle

Consider independent bond percolation with retention probability p on a spherically symmetric tree Γ. Write θΓ(p) for the probability that the root is in an infinite open cluster, and define the critical value pc=inf{p : θΓ(p)>0}. If θΓ(pc)=0, then the root may still percolate in the corresponding dynamical percolation process at the critical value pc, as demonstrated recently by Haggstrom, Peres, and Steif. Here we relate this phenomenon to the near-critical behavior of θΓ(p) by showing that the root percolates in the dynamical percolation process if and only if ∫(θΓ(p))−1 dp<∞. The “only if” direction extends to general trees, whereas the “if” direction fails in this generality. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 15, 311–318, 1999

考虑球对称树Γ上具有保留概率p的独立键渗透。用θΓ(p)表示根节点在无限开放簇中的概率，并定义临界值pc=inf{p: θΓ(p)>0}。如果θΓ(pc)=0，则在临界值pc处，根仍然可以在相应的动态渗流过程中进行渗流，最近由Haggstrom, Peres, and Steif证明。这里，我们通过证明当且仅当∫(θΓ(p))−1 dp<∞时，根在动态渗流过程中渗流，将这种现象与θΓ(p)的近临界行为联系起来。“only if”方向扩展到一般树，而“if”方向在这种一般性中失败。©1999 John Wiley & Sons, Inc随机结构。Alg。中华医学杂志，15,311-318,1999

引用次数: 5

The Tutte polynomial 图特多项式

Random Struct. Algorithms

Pub Date : 1999-10-01 DOI: 10.1002/(SICI)1098-2418(199910/12)15:3/4%3C210::AID-RSA2%3E3.0.CO;2-R

D. Welsh

This is a close approximation to the content of my lecture. After a brief survey of well known properties, I present some new interpretations relating to random graphs, lattice point enumeration, and chip firing games. I then examine complexity issues and concentrate in particular, on the existence of randomized approximation schemes. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 15, 210–228, 1999

引用次数: 243

Uniform boundedness of critical crossing probabilities implies hyperscaling 临界交叉概率的均匀有界性意味着超尺度

Random Struct. Algorithms

Pub Date : 1999-10-01 DOI: 10.1002/(SICI)1098-2418(199910/12)15:3/4%3C368::AID-RSA9%3E3.0.CO;2-B

C. Borgs, J. Chayes, H. Kesten, J. Spencer

We consider bond percolation on the d-dimensional hypercubic lattice. Assuming the existence of a single critical exponent, the exponent ρ describing the decay rate of point-to-plane crossings at the critical point, we prove that hyperscaling holds whenever critical rectangle crossing probabilities are uniformly bounded away from 1. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 15, 368–413, 1999

引用次数: 46

Mixing properties of the Swendsen-Wang process on classes of graphs 图类上Swendsen-Wang过程的混合性质

Random Struct. Algorithms

Pub Date : 1999-10-01 DOI: 10.1002/(SICI)1098-2418(199910/12)15:3/4%3C242::AID-RSA4%3E3.0.CO;2-C

C. Cooper, A. Frieze

We consider the mixing properties of the widely used Swendsen–Wang process for the Markov chain Monte Carlo estimation of the partition function of the ferromagnetic Q-state Potts model, for certain classes of graphs. In the paper “The Swendsen–Wang Process Does Not Always Mix Rapidly,” V. Gore and M. Jerrum obtained results for the mixing properties of the Swendsen–Wang process on the complete graph Kn. Our main results for graphs with n vertices are the following: For graphs with small maximum degree, the mixing time is polynomial in n for small enough values of the coupling constant β. For trees, the mixing time is O(n) for any β. For cycles, the mixing time is O(n log n) for any β. For random graphs Gn, p, p=Ω(n−1/3), there are values of the coupling constant β for which whp the Swendsen–Wang process does not mix rapidly. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 15, 242–261, 1999

我们考虑了广泛应用于铁磁q态Potts模型配分函数的马尔可夫链蒙特卡罗估计的Swendsen-Wang过程的混合性质。在论文“the Swendsen-Wang过程并不总是快速混合”中，V. Gore和M. Jerrum在完全图Kn上得到了Swendsen-Wang过程混合特性的结果。对于有n个顶点的图，我们的主要结果如下:对于最大度较小的图，在耦合常数β足够小的情况下，混合时间是n的多项式。对于树，对于任意β，混合时间为O(n)。对于循环，对于任意β，混合时间为O(n log n)。对于随机图Gn, p, p=Ω(n−1/3)，存在耦合常数β值，此时Swendsen-Wang过程不会快速混合。©1999 John Wiley & Sons, Inc随机结构。Alg。中华医学杂志，15,242-261,1999

引用次数: 58

The random bipartite nearest neighbor graphs 随机二部最近邻图

Random Struct. Algorithms

Pub Date : 1999-10-01 DOI: 10.1002/(SICI)1098-2418(199910/12)15:3/4%3C279::AID-RSA6%3E3.0.CO;2-J

B. Pittel, Robert S. Weishaar

The bipartite kth nearest neighbor graphs B are studied. It is shown that B k 1 has a limiting expected matching number of approximately 80% of its vertices, that with high Ž . probability whp B has at least 2 log nr13 log log n vertices not matched, and that whp B 2 3 does have a perfect matching. We also find a formula for the limiting probability that B is 2 connected and show that whp B is connected. Q 1999 John Wiley & Sons, Inc. Random Struct. 3 Alg., 15, 279]310, 1999

研究了二部第k近邻图B。结果表明，bk1的极限期望匹配数约为其顶点的80%，即高Ž。whp B至少有2个log nr13 log log n个不匹配的顶点，whp b23有完美匹配的概率。我们还找到了B是2连通的极限概率的公式，并证明了whp B是连通的。John Wiley & Sons, Inc.;随机结构。[j]中国科学:地球科学，1999

引用次数: 8

Intersecting random half cubes 与随机半立方体相交

Random Struct. Algorithms

Pub Date : 1999-10-01 DOI: 10.1002/(SICI)1098-2418(199910/12)15:3/4%3C436::AID-RSA11%3E3.0.CO;2-5

M. Talagrand

引用次数: 15

A sharp concentration inequality with applications 应用程序的集中度明显不平等

Random Struct. Algorithms

Pub Date : 1999-09-27 DOI: 10.1002/(SICI)1098-2418(200005)16:3%3C277::AID-RSA4%3E3.0.CO;2-1

S. Boucheron, G. Lugosi, P. Massart

We present a new general concentration-of-measure inequality and illustrate its power by applications in random combinatorics. The results find direct applications in some problems of learning theory.

我们提出了一个新的一般测度集中不等式，并通过在随机组合中的应用说明了它的威力。研究结果对学习理论的一些问题有直接的应用价值。

引用次数: 170

On k-connectivity for a geometric random graph 几何随机图的k-连通性

Random Struct. Algorithms

Pub Date : 1999-09-01 DOI: 10.1002/(SICI)1098-2418(199909)15:2%3C145::AID-RSA2%3E3.0.CO;2-G

M. Penrose

For n points uniformly randomly distributed on the unit cube in d dimensions, with d≥2, let ρn (respectively, σn) denote the minimum r at which the graph, obtained by adding an edge between each pair of points distant at most r apart, is k-connected (respectively, has minimum degree k). Then P[ρn=σn]1 as n∞. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 15, 145–164, 1999

引用次数: 474

A family of random trees with random edge lengths 一组具有随机边长的随机树

Random Struct. Algorithms

Pub Date : 1999-09-01 DOI: 10.1002/(SICI)1098-2418(199909)15:2%3C176::AID-RSA4%3E3.0.CO;2-4

D. Aldous, J. Pitman

We introduce a family of probability distributions on the space of trees with I labeled vertices and possibly extra unlabeled vertices of degree 3, whose edges have positive real lengths. Formulas for distributions of quantities such as degree sequence, shape, and total length are derived. An interpretation is given in terms of sampling from the inhomogeneous continuum random tree of Aldous and Pitman (1998). © 1999 John Wiley & Sons, Inc.

引用次数: 35

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