منابع مشابه
Heuristics for Semirandom Graph Problems
We consider semirandom graph models for nding large independent sets, colorings and bisections in graphs. These models generate problem instances by blending random and adversarial decisions. To generate semirandom independent set problems, an independent set S of n ver-tices is randomly chosen. Each edge connecting S with S is chosen with probability p, and an adversary is then allowed to add ...
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We study semirandom k-colorable graphs made up as follows. Partition the vertex set V = {1, . . . , n} randomly into k classes V1, . . . , Vk of equal size and include each Vi-Vj -edge with probability p independently (1 ≤ i < j ≤ k) to obtain a graph G0. Then, an adversary may add further Vi-Vj-edges (i 6= j) to G0, thereby completing the semirandom graph G = G∗n,p,k . We show that if np ≥ max...
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Alon, Krivelevich and Sudakov (Random Structures and Algorithms, 1998) designed an algorithm based on spectral techniques that almost surely nds a clique of size (p n) hidden in an otherwise random graph. We show that a diierent algorithm, based on the Lovv asz theta function, almost surely both nds the hidden clique and certiies its optimality. Our algorithm has an additional advantage of bein...
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1.1 Learning Mixtures of Gaussians We consider k distributions D1, D2, . . . , Dk on Rn. Suppose that Di has a mixing weight wi, where the mixing weights are nonnegative and sum to 1. We consider the following 2-stage sampling procedure (see Figure 1): first, we pick a distribution Di randomly according to the mixing weights; then we pick a random point x ∈ Rn according to Di. To illustrate the...
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Vertices of an affiliation network are linked to features and two vertices are declared adjacent whenever they share a common feature. We introduce a random intersection graph process aimed at modeling sparse evolving affiliation networks. We establish the asymptotic degree distribution and provide explicit asymptotic formulas for assortativity and clustering coefficients showing how these edge...
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ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2020
ISSN: 1042-9832,1098-2418
DOI: 10.1002/rsa.20887