Convergence theorems for some layout measures on random lattice and random geometric graphs

This work deals with convergence theorems and bounds on the cost of several layout measures for lattice graphs, random lattice graphs and sparse random geometric graphs. For full square lattices, we give optimal layouts for the problems still open. Our convergence theorems can be viewed as an analog...

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Detalhes bibliográficos
Autores: Díaz Cort, Josep|||0000-0003-4422-0067, Penrose, Matthew, Petit Silvestre, Jordi|||0000-0001-8331-8126, Serna Iglesias, María José|||0000-0001-9729-8648
Formato: informe técnico
Fecha de publicación:1999
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/93007
Acesso em linha:https://hdl.handle.net/2117/93007
Access Level:acceso abierto
Palavra-chave:Geometric graphs
Convergence theorems
Lattice graphs
Beardwood, Halton and Hammersley theorem
Subcritical regimes
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
Descrição
Resumo:This work deals with convergence theorems and bounds on the cost of several layout measures for lattice graphs, random lattice graphs and sparse random geometric graphs. For full square lattices, we give optimal layouts for the problems still open. Our convergence theorems can be viewed as an analogue of the Beardwood, Halton and Hammersley theorem for the Euclidian TSP on random points in the $d$-dimensional cube. As the considered layout measures are non-subadditive, we use percolation theory to obtain our results on random lattices and random geometric graphs. In particular, we deal with the subcritical regimes on these class of graphs.