Theoretical Computer Science
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
Piecemeal Learning of an Unknown Environment
Machine Learning - Special issue on COLT '93
Piecemeal graph exploration by a mobile robot (extended abstract)
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
Navigating in Unfamiliar Geometric Terrain
SIAM Journal on Computing
How to learn an unknown environment. I: the rectilinear case
Journal of the ACM (JACM)
The power of a pebble: exploring and mapping directed graphs
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Randomized robot navigation algorithms
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Exploring unknown undirected graphs
Journal of Algorithms
Exploring Unknown Environments
SIAM Journal on Computing
Optimal constrained graph exploration
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Journal of Graph Theory
Optimal Graph Exploration without Good Maps
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Can we elect if we cannot compare?
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Optimal graph exploration without good maps
Theoretical Computer Science
Distributed chasing of network intruders
Theoretical Computer Science
Remembering without memory: Tree exploration by asynchronous oblivious robots
Theoretical Computer Science
Computing without communicating: ring exploration by asynchronous oblivious robots
OPODIS'07 Proceedings of the 11th international conference on Principles of distributed systems
Labeling schemes for tree representation
IWDC'05 Proceedings of the 7th international conference on Distributed Computing
Label-guided graph exploration by a finite automaton
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Space lower bounds for graph exploration via reduced automata
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
The reduced automata technique for graph exploration space lower bounds
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 robot with k-bit memory has to explore a tree whose nodes are unlabeled and edge ports are locally labeled at each node. The robot has no a priori knowledge of the topology of the tree or of its size, and its aim is to traverse all the edges. While O(logΔ) bits of memory suffice to explore any tree of maximum degree Δ if stopping is not required, we show that bounded memory is not sufficient to explore with stop all trees of bounded degree (indeed Ω(log log log n) bits of memory are needed for some such trees of size n). For the more demanding task requiring to stop at the starting node after completing exploration, we show a sharper lower bound Ω(log n) on required memory size, and present an algorithm to accomplish this task with O(log2 n)-bit memory, for all n-node trees.