COHEN, Reuven; FRAIGNIAUD, Pierre; ILCINKAS, David; KORMAN, Amos; PELEG, David

doi:10.1145/1383369.1383373

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COHEN, Reuven
Department of Electrical and Computer Engineering [Boston University] [ECE]

FRAIGNIAUD, Pierre
Laboratoire d'informatique Algorithmique : Fondements et Applications [LIAFA]

ILCINKAS, David
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]

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Ce document a été publié dans

ACM Transactions on Algorithms. 2008-08, vol. 4, n° 4, p. Article 42

Association for Computing Machinery

Résumé en anglais

A finite automaton, simply referred to as a {\em robot}, has to explore a graph, i.e., visit all the nodes of the graph. The robot has no a priori knowledge of the topology of the graph or of its size. It is known that, for any $k$-state robot, there exists a graph of maximum degree~3 that the robot cannot explore. This paper considers the effects of allowing the system designer to add short labels to the graph nodes in a preprocessing stage, and using these labels to guide the exploration by the robot. We describe an exploration algorithm that given appropriate 2-bit labels (in fact, only 3-valued labels) allows a robot to explore all graphs. Furthermore, we describe a suitable labeling algorithm for generating the required labels, in linear time. We also show how to modify our labeling scheme so that a robot can explore all graphs of bounded degree, given appropriate 1-bit labels. In other words, although there is no robot able to explore all graphs of maximum degree~3, there is a robot $\cR$, and a way to color in black or white the nodes of any bounded-degree graph $G$, so that $\cR$ can explore the colored graph $G$. Finally, we give impossibility results regarding graph exploration by a robot with no internal memory (i.e., a single state automaton).< Réduire

Mots clés en anglais

Distributed algorithms

Graph exploration

Labeling schemes

URI

https://oskar-bordeaux.fr/handle/20.500.12278/198617

DOI

http://dx.doi.org/10.1145/1383369.1383373

Project ANR

Algorithm Design and Analysis for Implicitly and Incompletely Defined Interaction Networks - ANR-07-BLAN-0322

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Importé de hal

Unités de recherche

Laboratoire Bordelais de Recherche en Informatique (LaBRI) - UMR 5800