Computing with snakes in directed networks of automata
Journal of Algorithms
On mixed connectivity certificates
ESA '95 Selected papers from the third European symposium on Algorithms
Tree exploration with little memory
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
The power of a pebble: exploring and mapping directed graphs
Information and Computation
Universal Traversal Sequences with Backtracking
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Undirected ST-connectivity in log-space
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
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 power of team exploration: two robots can learn unlabeled directed graphs
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Space lower bounds for graph exploration via reduced automata
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
Fast periodic graph exploration with constant memory
Journal of Computer and System Sciences
Quiescence of self-stabilizing gossiping among mobile agents in graphs
Theoretical Computer Science
Fast periodic graph exploration with constant memory
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
On the self-stabilization of mobile robots in graphs
OPODIS'07 Proceedings of the 11th international conference on Principles of distributed systems
More efficient periodic traversal in anonymous undirected graphs
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
Periodic data retrieval problem in rings containing a malicious host
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
More efficient periodic traversal in anonymous undirected graphs
Theoretical Computer Science
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We consider the task of exploring graphs with anonymous nodes by a team of non-cooperative robots, modeled as finite automata. For exploration to be completed, each edge of the graph has to be traversed by at least one robot. In this paper, the robots have no a priori knowledge of the topology of the graph, nor of its size, and we are interested in the amount of memory the robots need to accomplish exploration, We introduce the so-called reduced automata technique, and we show how to use this technique for deriving several space lower bounds for exploration. Informally speaking, the reduced automata technique consists in reducing a robot to a simpler form that preserves its “core” behavior on some graphs. Using this technique, we first show that any set of q≥ 1 non-cooperative robots, requires $\Omega(\log(\frac{n}{q}))$ memory bits to explore all n-node graphs. The proof implies that, for any set of qK-state robots, there exists a graph of size O(qK) that no robot of this set can explore, which improves the O(KO(q)) bound by Rollik (1980). Our main result is an application of this latter result, concerning terminating graph exploration with one robot, i.e., in which the robot is requested to stop after completing exploration. For this task, the robot is provided with a pebble, that it can use to mark nodes (without such a marker, even terminating exploration of cycles cannot be achieved). We prove that terminating exploration requires Ω(log n) bits of memory for a robot achieving this task in all n-node graphs.