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Revista Colombiana de Matemáticas

versión impresa ISSN 0034-7426

Rev.colomb.mat. v.41  supl.1 Bogotá oct. 2007

 

Network tomography

CARLOS A. BERENSTEIN1, FRANKLIN GAVILÁNEZ2

1 Department of Mathematics, University of Maryland, Maryland, USA. E-mail: carlos@math.umd.edu
2 Institute for Systems Research, University of Maryland, Maryland, USA. E-mail: fgavilan@math.umd.edu


Abstract

While conventional tomography is associated to the Radon transform in Euclidean spaces, electrical impedance tomography, or EIT, is associated to the Radon transform in the hyperbolic plane. We discuss some recent work on network tomography that can be associated to a problem similar to EIT on graphs and indicate how in some sense it may be also associated to the Radon transform on trees.

Key words: Network monitoring, inverse problems in finite graphs and trees, Radon transform


2000 Mathematics Subject Classification: Primary: 05C40, 35R30. Secondary: 94C12.

Resumen

Mientras la tomografía convencional es asociada a la transformada de Radon en espacios Euclídeos, la tomografía de impedancia eléctrica, o EIT, es asociada a la transformada de Radón en el plano hiperbólico. Aquí exponemos nuestro más reciente trabajo sobre tomografía de redes que puede ser asociado a un problema similar a EIT en grafos y también, en cierto sentido, a la transformada de Radon en árboles.

Palabras clave: Red de monitoreo, problemas inversos en grafos y árboles finitos, transformada de Radon.


Texto completo disponible en PDF


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