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

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hdl:2117/93007

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Díaz Cort, JosepMés informacióMés informacióMés informació
Penrose, Matthew
Petit Silvestre, JordiMés informacióMés informacióMés informació
Serna Iglesias, María JoséMés informacióMés informacióMés informació
Document typeResearch report
Defense date1999-04
Rights accessOpen Access
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
Abstract
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.
CitationDiaz, J., Penrose, M., Petit, J., Serna, M. "Convergence theorems for some layout measures on random lattice and random geometric graphs". 1999. 
Is part ofLSI-99-10-R
URIhttp://hdl.handle.net/2117/93007
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