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GODARD-2009-448749

Emmanuel Godard, Yves Métivier, Gerard Tel. Termination Detection of Local Computations. December 2009.

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Abstract

Contrary to the sequential world, the processes involved in a distributed system do not necessarily know when a computation is globally finished. This paper investigates the problem of the detection of the termination of local computations. We define four types of termination detection: no detection, detection of the local termination, detection by a distributed observer, detection of the global termination. We give a complete characterisation (except in the local termination detection case where a partial one is given) for each of this termination detection and show that they define a strict hierarchy. These results emphasise the difference between computability of a distributed task and termination detection. Furthermore, these characterisations encompass all standard criteria that are usually formulated : topological restriction (tree, rings, or triangu- lated networks ...), topological knowledge (size, diameter ...), and local knowledge to distinguish nodes (identities, sense of direction). These results are now presented as corollaries of generalising theorems. As a very special and important case, the techniques are also applied to the election problem. Though given in the model of local computations, these results can give qualitative insight for similar results in other standard models. The necessary conditions involve graphs covering and quasi-covering; the sufficient conditions (constructive local computations) are based upon an enumeration algorithm of Mazurkiewicz and a stable properties detection algorithm of Szymanski, Shi and Prywes

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Emmanuel Godard
Yves Métivier
Gerard Tel

BibTex Reference

@TechReport{GODARD-2009-448749,
   Author = {Godard, Emmanuel and Métivier, Yves and Tel, Gerard},
   Title = {Termination Detection of Local Computations},
   Month = {December},
   Year = {2009}
}

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