Efficiently searching a graph by a smell-oriented vertex process
Annals of Mathematics and Artificial Intelligence
Robotic Exploration, Brownian Motion and Electrical Resistance
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
Memory Efficient Anonymous Graph Exploration
Graph-Theoretic Concepts in Computer Science
Tight Bounds for the Cover Time of Multiple Random Walks
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Expansion and the cover time of parallel random walks
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Tight bounds for the cover time of multiple random walks
Theoretical Computer Science
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Aleliunas et al. [20th Annual Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1979, pp. 218--223] posed the following question: "The reachability problem for undirected graphs can be solved in log space and $O(mn)$ time [$m$ is the number of edges and $n$ is the number of vertices] by a probabilistic algorithm that simulates a random walk, or in linear time and space by a conventional deterministic graph traversal algorithm. Is there a spectrum of time-space trade-offs between these extremes?" This question is answered in the affirmative for sparse graphs by presentation of an algorithm that is faster than the random walk by a factor essentially proportional to the size of its workspace. For denser graphs, this algorithm is faster than the random walk but the speed-up factor is smaller.