Random Structures & Algorithms
The power of a pebble: exploring and mapping directed graphs
Information and Computation
Universal traversal sequences with backtracking
Journal of Computer and System Sciences - Complexity 2001
Randomization and Derandomization in Space-Bounded Computation
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
The cover time, the blanket time, and the Matthews bound
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Undirected ST-connectivity in log-space
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Graph exploration by a finite automaton
Theoretical Computer Science - Mathematical foundations of computer science 2004
Tree exploration with logarithmic memory
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Deterministic random walks on regular trees
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Journal of Graph Theory
Random walks, universal traversal sequences, and the complexity of maze problems
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
The hitting and cover times of random walks on finite graphs using local degree information
Theoretical Computer Science
Deterministic random walks on the two-dimensional grid
Combinatorics, Probability and Computing
Easy and hard testbeds for real-time search algorithms
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Robustness of the Rotor-router Mechanism
OPODIS '09 Proceedings of the 13th International Conference on Principles of Distributed Systems
The cover time of deterministic random walks
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
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We consider the problem of exploring an anonymous undirected graph using an oblivious robot. The studied exploration strategies are designed so that the next edge in the robot's walk is chosen using only local information, and so that some local equity (fairness) criterion is satisfied for the adjacent undirected edges. Such strategies can be seen as an attempt to derandomize random walks, and are natural undirected counterparts of the rotor-router model for symmetric directed graphs. The first of the studied strategies, known as Oldest-First (OF), always chooses the neighboring edge for which the most time has elapsed since its last traversal. Unlike in the case of symmetric directed graphs, we show that such a strategy in some cases leads to exponential cover time. We then consider another strategy called Least-Used-First (LUF) which always uses adjacent edges which have been traversed the smallest number of times. We show that any Least-Used-First exploration covers a graph G = (V ,E ) of diameter $\mathit{D}$ within time $O(\mathit{D}|E|)$, and in the long run traverses all edges of G with the same frequency.