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Communication Dans Un Congrès Année : 2005

Space Lower Bounds for Graph Exploration via Reduced Automata

Résumé

We consider the task of exploring graphs with anonymous nodes by a team of non-cooperative robots modeled as finite automata. These robots have no \emph{a priori} knowledge of the topology of the graph, or of its size. Each edge has to be traversed by at least one robot. We first show that, for any set of $q$ non-cooperative $K$-state robots, there exists a graph of size $O(qK)$ that no robot of this set can explore. This improves the $O(K^{O(q)})$ bound by Rollik (1980). Our main result is an application of this improvement. It concerns exploration with stop, in which one robot has to explore and stop after completing exploration. For this task, the robot is provided with a pebble, that it can use to mark nodes. We prove that exploration with stop requires $\Omega(\log n)$ bits for the family of graphs with at most $n$ nodes. On the other hand, we prove that there exists an exploration with stop algorithm using a robot with $O(D \log \Delta)$ bits of memory to explore all graphs of diameter at most $D$ and degree at most $\Delta$.
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Dates et versions

hal-00339766 , version 1 (18-11-2008)

Identifiants

Citer

Pierre Fraigniaud, David Ilcinkas, Sergio Rajsbaum, Sébastien Tixeuil. Space Lower Bounds for Graph Exploration via Reduced Automata. SIROCCO 2005, May 2005, Le Mont Saint-Michel, France. pp.140-154, ⟨10.1007/11429647_13⟩. ⟨hal-00339766⟩
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