Abstract
This paper is a contribution to understanding the power and the limitations of asynchronous local computations on graphs and networks. We use local computations to define a notion of graph recognition, in particular our model enables a simulation of finite automata on words and on trees. We introduce the notion of k-covering to examine limitations of such systems. For example we prove that we cannot recognize the families of series parallel graphs and planar graphs by means of local computations.
This research has been supported by the P.R.C. Mathématiques et Informatique and ESPRIT Basic Research Action 3166 ASMICS
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Litovsky, I., Métivier, Y., Zielonka, W. (1993). The power and the limitations of local computations on graphs. In: Mayr, E.W. (eds) Graph-Theoretic Concepts in Computer Science. WG 1992. Lecture Notes in Computer Science, vol 657. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56402-0_58
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DOI: https://doi.org/10.1007/3-540-56402-0_58
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