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...
| Autores: | , , , |
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| 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 |
| 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. |
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