Limit theory of combinatorial optimization for random geometric graphs
نویسندگان
چکیده
In the random geometric graph G(n,rn), n vertices are placed randomly in Euclidean d-space and edges added between any pair of distant at most rn from each other. We establish strong laws large numbers (LLNs) for a class parameters, evaluated G(n,rn) thermodynamic limit with nrnd= const., also dense nrnd→∞, rn→0. Examples include domination number, independence clique-covering eternal number triangle packing number. The general theory is based on certain subadditivity superadditivity properties, yields LLNs other functionals such as minimum weight traveling salesman, spanning tree, matching, bipartite matching salesman problems, functions polynomial growth order d−ε, under scaling distance parameter.
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ژورنال
عنوان ژورنال: Annals of Applied Probability
سال: 2021
ISSN: ['1050-5164', '2168-8737']
DOI: https://doi.org/10.1214/20-aap1661