贪心搜索算法在Erdös-Rényi图上的大偏差原理

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2020-07-09 DOI:10.30757/alea.v19-16

P. Bermolen, Valeria Goicoechea, M. Jonckheere, E. Mordecki

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引用次数: 4

摘要

我们在Erdos-Renyi (ER)图上证明了一个贪婪探索过程的大偏差原理(LDP)，当节点数量到达这个http URL时，证明了我们的主要结果。我们使用Feng和Kurtz(2006)提出的研究大偏差过程的一般策略，该策略基于非线性半群的收敛性。速率函数可以用封闭形式的公式表示，提供大偏差的轨迹可以明确地解决相关的优化问题。此外，我们还导出了由该算法发现的最大独立集的大小的LDP，并分析了它超过已知最大独立集的边界的概率。我们还分析了这些结果与独立集的景观复杂性和探索动态之间的联系。

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Large Deviation Principle for the Greedy Exploration Algorithm over Erdös-Rényi Graphs

We prove a large deviation principle (LDP) for a greedy exploration process on an Erdos-Renyi (ER) graph when the number of nodes goes to this http URL prove our main result we use the general strategy for the study of large deviations of processes proposed by Feng and Kurtz (2006), which is based on the convergence of non-linear semigroups. The rate function can be expressed in a closed form formula and associated optimization problems can be solved explicitly providing the trajectory of the large deviation. In addition we derive a LDP for the size of the maximum independent set discovered by such algorithm and analyze the probability that it exceeds known bounds for the maximal independent set. We also analyze the link between these results and the landscape complexity of the independent set and the exploration dynamic.

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来源期刊

Alea-Latin American Journal of Probability and Mathematical Statistics STATISTICS & PROBABILITY-

CiteScore

1.10

自引率

0.00%

发文量

期刊介绍： ALEA publishes research articles in probability theory, stochastic processes, mathematical statistics, and their applications. It publishes also review articles of subjects which developed considerably in recent years. All articles submitted go through a rigorous refereeing process by peers and are published immediately after accepted. ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs. Authors are allowed to deposit their published article into their institutional repository, freely and with no embargo, as long as they acknowledge the source of the paper. ALEA is affiliated with the Institute of Mathematical Statistics.