Tree exploration with little memory
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
The power of a pebble: exploring and mapping directed graphs
Information and Computation
The power of team exploration: two robots can learn unlabeled directed graphs
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Tree exploration with logarithmic memory
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Label-guided graph exploration by a finite automaton
ACM Transactions on Algorithms (TALG)
On the Power of Local Orientations
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
Anonymous graph exploration without collision by mobile robots
Information Processing Letters
On the Solvability of Anonymous Partial Grids Exploration by Mobile Robots
OPODIS '08 Proceedings of the 12th International Conference on Principles of Distributed Systems
Tree exploration with logarithmic memory
ACM Transactions on Algorithms (TALG)
Improved distributed exploration of anonymous networks
ICDCN'06 Proceedings of the 8th international conference on Distributed Computing and Networking
Smart robot teams exploring sparse trees
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
The reduced automata technique for graph exploration space lower bounds
Theoretical Computer Science
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We consider the task of exploring graphs with anonymous nodes by a team of non-cooperative robots modeled as finite automata. These robots have no a priori knowledge of the topology of the graph, or of its size. Each edge has to be traversed by at least one robot. We first show that, for any set of q non-cooperative K-state robots, there exists a graph of size O(qK) that no robot of this set can explore. This improves the O(KO(q)) bound by Rollik (1980). Our main result is an application of this improvement. It concerns exploration with stop, in which one robot has to explore and stop after completing exploration. For this task, the robot is provided with a pebble, that it can use to mark nodes. We prove that exploration with stop requires Ω(log n) bits for the family of graphs with at most n nodes. On the other hand, we prove that there exists an exploration with stop algorithm using a robot with O(D log Δ) bits of memory to explore all graphs of diameter at most D and degree at most Δ.