Tree exploration with little memory
Journal of Algorithms
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Graph exploration by a finite automaton
Theoretical Computer Science - Mathematical foundations of computer science 2004
Oracle size: a new measure of difficulty for communication tasks
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
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
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
Space lower bounds for graph exploration via reduced automata
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
Exploration of Periodically Varying Graphs
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Almost optimal asynchronous rendezvous in infinite multidimensional grids
DISC'10 Proceedings of the 24th international conference on Distributed computing
Tree exploration with logarithmic memory
ACM Transactions on Algorithms (TALG)
Toward more localized local algorithms: removing assumptions concerning global knowledge
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Journal of Parallel and Distributed Computing
More efficient periodic traversal in anonymous undirected graphs
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
Black hole search in directed graphs
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
Periodic data retrieval problem in rings containing a malicious host
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
More efficient periodic traversal in anonymous undirected graphs
Theoretical Computer Science
On the exploration of time-varying networks
Theoretical Computer Science
Memory lower bounds for randomized collaborative search and implications for biology
DISC'12 Proceedings of the 26th international conference on Distributed Computing
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A finite automaton, simply referred to as a robot, 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 k-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 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).