噪声随机几何图的团数

IF 0.9 3区数学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Random Structures & Algorithms Pub Date : 2022-08-22 DOI:10.1002/rsa.21134

Matthew Kahle, Minghao Tian, Yusu Wang

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引用次数: 3

摘要

设Gn $$ {G}_n $$为随机几何图，然后对于q,p∈[0,1)$$ q,p\in \left[0,1\right) $$，我们构造一个(q,p) $$ \left(q,p\right) $$‐摄动噪声随机几何图Gnq,p $$ {G}_n^{q,p} $$，其中Gn $$ {G}_n $$中每条存在的边以概率q $$ q $$被移除，而Gn $$ {G}_n $$中每条不存在的边以概率p $$ p $$被插入。我们给出了若干参数区团数ωGnq,p $$ \omega \left({G}_n^{q,p}\right) $$的渐近紧界。

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On the clique number of noisy random geometric graphs

Let Gn$$ {G}_n $$ be a random geometric graph, and then for q,p∈[0,1)$$ q,p\in \left[0,1\right) $$ we construct a (q,p)$$ \left(q,p\right) $$ ‐perturbed noisy random geometric graph Gnq,p$$ {G}_n^{q,p} $$ where each existing edge in Gn$$ {G}_n $$ is removed with probability q$$ q $$ , while and each non‐existent edge in Gn$$ {G}_n $$ is inserted with probability p$$ p $$ . We give asymptotically tight bounds on the clique number ωGnq,p$$ \omega \left({G}_n^{q,p}\right) $$ for several regimes of parameter.

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来源期刊

Random Structures & Algorithms 数学-计算机：软件工程

CiteScore

2.50

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： It is the aim of this journal to meet two main objectives: to cover the latest research on discrete random structures, and to present applications of such research to problems in combinatorics and computer science. The goal is to provide a natural home for a significant body of current research, and a useful forum for ideas on future studies in randomness. Results concerning random graphs, hypergraphs, matroids, trees, mappings, permutations, matrices, sets and orders, as well as stochastic graph processes and networks are presented with particular emphasis on the use of probabilistic methods in combinatorics as developed by Paul Erdõs. The journal focuses on probabilistic algorithms, average case analysis of deterministic algorithms, and applications of probabilistic methods to cryptography, data structures, searching and sorting. The journal also devotes space to such areas of probability theory as percolation, random walks and combinatorial aspects of probability.