Label-guided graph exploration by a finite automaton

Reuven Cohen, Pierre Fraigniaud, David Ilcinkas, Amos Korman, David Peleg

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


A finite automaton, simply referred to as a 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 (k+1)-node 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 R, and a way to color in black or white the nodes of any bounded-degree graph G, so that R. 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).

Original languageEnglish
Title of host publicationICALP 2005
Subtitle of host publicationAutomata, Languages and Programming
Number of pages12
StatePublished - 2005
Externally publishedYes
Event32nd International Colloquium on Automata, Languages and Programming, ICALP 2005 - Lisbon, Portugal
Duration: 11 Jul 200515 Jul 2005

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Verlag
ISSN (Print)0302-9743


Conference32nd International Colloquium on Automata, Languages and Programming, ICALP 2005

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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