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Holographic Trees

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LATIN 2002: Theoretical Informatics (LATIN 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2286))

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Abstract

It is known that computations of anonymous networks can be reduced to the construction of a certain graph, the minimum base of the network. The crucial step of this construction is the inference of the minimum base from a finite tree that each processor can build (its truncated view). We isolate those trees that make this inference possible, and call them holographic. Intuitively, a tree is holographic if it is enough self-similar to be uniquely extendible to an infinite tree. This possibility depends on a size function for the class of graphs under examination, which we call a holographic bound for the class. Holographic bounds give immediately, for instance, bounds for the quiescence time of self-stabilizing protocols. In this paper we give weakly tight holographic bounds for some classes of graphs.

The authors have been partially supported by the Italian MURST (Finanziamento di iniziative di ricerca “diffusa” condotte da parte di giovani ricercatori).

Our graphs are directed, and may possess multiple arcs and loops-see Sect. 2.

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Author information

Authors and Affiliations

  1. Dipartimento di Scienze dell’Informazione, Universitá degli Studi di Milano, Via Comelico 39/41, I-20135, Milano, MI, Italy

    Paolo Boldi & Sebastiano Vigna

Authors
  1. Paolo Boldi
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  2. Sebastiano Vigna
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Editor information

Editors and Affiliations

  1. Compaq Cambridge Research Laboratory, One Cambridge Center, 02142-1612, Cambridge, MA, USA

    Sergio Rajsbaum

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© 2002 Springer-Verlag Berlin Heidelberg

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Boldi, P., Vigna, S. (2002). Holographic Trees. In: Rajsbaum, S. (eds) LATIN 2002: Theoretical Informatics. LATIN 2002. Lecture Notes in Computer Science, vol 2286. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45995-2_41

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  • DOI: https://doi.org/10.1007/3-540-45995-2_41

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43400-9

  • Online ISBN: 978-3-540-45995-8

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