On the relation between graph distance and Euclidean distance in random geometric graphs

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dc.contributor	Universitat Politècnica de Catalunya. Departament de Ciències de la Computació
dc.contributor	Universitat Politècnica de Catalunya. ALBCOM - Algorismia, Bioinformàtica, Complexitat i Mètodes Formals
dc.contributor	Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
dc.contributor.author	Díaz Cort, Josep
dc.contributor.author	Dieter Wilhelm, Mitsche
dc.contributor.author	Perarnau Llobet, Guillem
dc.contributor.author	Pérez Giménez, Xavier
dc.date	2016-09-01
dc.identifier.citation	Diaz, J., Dieter, M., Perarnau-Llobet, G., Pérez-Giménez, X. On the relation between graph distance and Euclidean distance in random geometric graphs. "Advances in applied probability", 1 Setembre 2016, vol. 48, núm. 3, p. 848-864.
dc.identifier.citation	0001-8678
dc.identifier.citation	10.1017/apr.2016.31
dc.identifier.uri	http://hdl.handle.net/2117/115054
dc.language.iso	eng
dc.relation	https://www.cambridge.org/core/journals/advances-in-applied-probability/article/div-classtitleon-the-relation-between-graph-distance-and-euclidean-distance-in-random-geometric-graphsdiv/2A5D7775A19265E42A8090A5ED981551
dc.rights	Attribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Probabilitat
dc.subject	Random geometric graph
dc.subject	graph distance
dc.subject	Euclidean distance
dc.subject	diameter
dc.subject	Classificació AMS::60 Probability theory and stochastic processes::60D05 Geometric probability, stochastic geometry, random sets
dc.title	On the relation between graph distance and Euclidean distance in random geometric graphs
dc.type	info:eu-repo/semantics/submittedVersion
dc.type	info:eu-repo/semantics/article
dc.description.abstract	Given any two vertices u, v of a random geometric graph G(n, r), denote by dE(u, v) their Euclidean distance and by dE(u, v) their graph distance. The problem of finding upper bounds on dG(u, v) conditional on dE(u, v) that hold asymptotically almost surely has received quite a bit of attention in the literature. In this paper we improve the known upper bounds for values of r=¿(vlogn) (that is, for r above the connectivity threshold). Our result also improves the best known estimates on the diameter of random geometric graphs. We also provide a lower bound on dE(u, v) conditional on dE(u, v).
dc.description.abstract	Peer Reviewed

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