Optimal distributed algorithms in unlabeled tori and chordal rings
Journal of Parallel and Distributed Computing
The power of a pebble: exploring and mapping directed graphs
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Exploring unknown undirected graphs
Journal of Algorithms
Exploring Unknown Environments
SIAM Journal on Computing
Optimal Graph Exploration without Good Maps
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Distributed Computing
Tree exploration with little memory
Journal of Algorithms
Journal of Graph Theory
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
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In this paper we consider the map construction problem in the case of an anonymous, unoriented torus of unknown size. An agent that can move from node to neighbouring node in the torus is initially placed in an arbitrary node and has to construct an edge-labeled map. In other words, it has to draw, in its local memory, an edge-labeled torus isomorphic to the one it is moving on. The agent has enough local memory to represent the torus and one or two tokens that can be dropped on and picked up from nodes. Efficiency is measured in terms of number of moves performed by the agent. When the agent has no token available, the problem is clearly unsolvable. In the paper we show that, when the agent has one token available there exists an optimal algorithm for constructing the map of the torus; the agent, in fact, performs Θ(N) moves (where N is the number of nodes of the torus). Before showing the optimal solution with the optimal number of tokens, we describe a simpler solution that works when two tokens are available, we then modify it to obtain the same bound when the agent has only one token available.