Artificial Intelligence
The cover time of a regular expander is O(n log n)
Information Processing Letters
On the time to traverse all edges of a graph
Information Processing Letters
A technique for lower bounding the cover time
SIAM Journal on Discrete Mathematics
A tight lower bound on the cover time for random walks on graphs
Random Structures & Algorithms
Local Divergence of Markov Chains and the Analysis of Iterative Load-Balancing Schemes
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
On Playing Golf with Two Balls
SIAM Journal on Discrete Mathematics
The Cover Time of Random Regular Graphs
SIAM Journal on Discrete Mathematics
Simulating a Random Walk with Constant Error
Combinatorics, Probability and Computing
Tree exploration with logarithmic memory
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Deterministic random walks on the integers
European Journal of Combinatorics
Deterministic random walks on regular trees
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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 cover time of the giant component of a random graph
Random Structures & Algorithms
Undirected connectivity in log-space
Journal of the ACM (JACM)
The cover time of random geometric graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Deterministic random walks on the two-dimensional grid
Combinatorics, Probability and Computing
Near-perfect load balancing by randomized rounding
Proceedings of the forty-first annual ACM symposium on Theory of computing
Derandomizing Random Walks in Undirected Graphs Using Locally Fair Exploration Strategies
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Euler tour lock-in problem in the rotor-router model: i choose pointers and you choose port numbers
DISC'09 Proceedings of the 23rd international conference on Distributed computing
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
The multi-agent rotor-router on the ring: a deterministic alternative to parallel random walks
Proceedings of the 2013 ACM symposium on Principles of distributed computing
Parallel rotor walks on finite graphs and applications in discrete load balancing
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
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The rotor router model is a popular deterministic analogue of a random walk on a graph. Instead of moving to a random neighbor, the neighbors are served in a fixed order. We examine how fast this "deterministic random walk" covers all vertices (or all edges). We present general techniques to derive upper bounds for the vertex and edge cover time and derive matching lower bounds for several important graph classes. Depending on the topology, the deterministic random walk can be asymptotically faster, slower or equally fast compared to the classical random walk.