TY - JOUR

T1 - Label-guided graph exploration by a finite automaton

AU - Cohen, Reuven

AU - Fraigniaud, Pierre

AU - Ilcinkas, David

AU - Korman, Amos

AU - Peleg, David

PY - 2005

Y1 - 2005

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=26444483301&partnerID=8YFLogxK

U2 - 10.1007/11523468_28

DO - 10.1007/11523468_28

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AN - SCOPUS:26444483301

SN - 0302-9743

VL - 3580

SP - 335

EP - 346

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

T2 - 32nd International Colloquium on Automata, Languages and Programming, ICALP 2005

Y2 - 11 July 2005 through 15 July 2005

ER -