Label-guided graph exploration by a finite automaton
-
- Reuven Cohen
- Boston University, Boston, MA
-
- Pierre Fraigniaud
- CNRS and Université Paris Diderot, Paris, France
-
- David Ilcinkas
- CNRS and Université Bordeaux I, France
-
- Amos Korman
- CNRS and Université Paris Diderot, Paris, France
-
- David Peleg
- The Weizmann Institute, Rehovot, Israel
Abstract
<jats:p> A finite automaton, simply referred to as a <jats:italic>robot</jats:italic> , has to explore a graph, that is, visit all the nodes of the graph. The robot has no a priori knowledge of the topology of the graph, nor of its size. It is known that for any <jats:italic>k</jats:italic> -state robot, there exists a graph of maximum degree 3 that the robot cannot explore. This article considers the effects of allowing the system designer to add short labels to the graph nodes in a preprocessing stage, for helping 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 <jats:italic>G</jats:italic> , so that R can explore the colored graph <jats:italic>G</jats:italic> . Finally, we give impossibility results regarding graph exploration by a robot with no internal memory (i.e., a single-state automaton). </jats:p>
Journal
-
- ACM Transactions on Algorithms
-
ACM Transactions on Algorithms 4 (4), 1-18, 2008-08
Association for Computing Machinery (ACM)
- Tweet
Details 詳細情報について
-
- CRID
- 1363951795271593472
-
- ISSN
- 15496333
- 15496325
-
- Data Source
-
- Crossref