Abstract
AbstractWe review the space complexity of deterministically exploring undirected graphs. We assume that vertices are indistinguishable and that edges have a locally unique color that guides the traversal of a space-constrained agent. The graph is considered to be explored once the agent has visited all vertices. We visit results for this setting showing that $$\varTheta \,(\log n)$$
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bits of memory are necessary and sufficient for an agent to explore all n-vertex graphs. We then illustrate that, if agents only have sublogarithmic memory, the number of (distinguishable) agents needed for collaborative exploration is $$\varTheta \,(\log \log n)$$
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Publisher
Springer Nature Switzerland