Tree exploration with little memory
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the 4th GI-Conference on Theoretical Computer Science
On the power of the compass (or, why mazes are easier to search than graphs)
SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of Computer Science
Local MST computation with short advice
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Tree exploration with logarithmic memory
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Distributed chasing of network intruders
Theoretical Computer Science
Fast periodic graph exploration with constant memory
Journal of Computer and System Sciences
Note: Setting port numbers for fast graph exploration
Theoretical Computer Science
Memory Efficient Anonymous Graph Exploration
Graph-Theoretic Concepts in Computer Science
Online Computation with Advice
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Fast periodic graph exploration with constant memory
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
DISC'10 Proceedings of the 24th international conference on Distributed computing
Online computation with advice
Theoretical Computer Science
Improved distributed exploration of anonymous networks
ICDCN'06 Proceedings of the 8th international conference on Distributed Computing and Networking
Setting port numbers for fast graph exploration
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Labeling schemes for tree representation
IWDC'05 Proceedings of the 7th international conference on Distributed Computing
Distributed computing with advice: information sensitivity of graph coloring
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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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 ${\mathcal R}$, and a way to color in black or white the nodes of any bounded-degree graph G, so that ${\mathcal R}$ 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).