Distributed Anonymous Mobile Robots: Formation of Geometric Patterns
SIAM Journal on Computing
Piecemeal graph exploration by a mobile robot
Information and Computation
Exploring Unknown Environments
SIAM Journal on Computing
Optimal deterministic protocols for mobile robots on a grid
Information and Computation
Graph exploration by a finite automaton
Theoretical Computer Science - Mathematical foundations of computer science 2004
Collision prevention using group communication for asynchronous cooperative mobile robots
AINA '07 Proceedings of the 21st International Conference on Advanced Networking and Applications
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
Fast periodic graph exploration with constant memory
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
Computing without communicating: ring exploration by asynchronous oblivious robots
OPODIS'07 Proceedings of the 11th international conference on Principles of distributed systems
Setting port numbers for fast graph exploration
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Finding short right-hand-on-the-wall walks in graphs
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
Space lower bounds for graph exploration via reduced automata
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
On the Solvability of Anonymous Partial Grids Exploration by Mobile Robots
OPODIS '08 Proceedings of the 12th International Conference on Principles of Distributed Systems
Uniform multi-agent deployment on a ring
Theoretical Computer Science
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Considering autonomous mobile robots moving on a finite anonymous graph, this paper focuses on the Constrained Perpetual Graph Exploration problem (CPGE). That problem requires each robot to perpetually visit all the vertices of the graph, in such a way that no vertex hosts more than one robot at a time, and each edge is traversed by at most one robot at a time. The paper states an upper bound k on the number of robots that can be placed in the graph while keeping CPGE solvability. To make the impossibility result as strong as possible (no more than k robots can be initially placed in the graph), this upper bound is established under a strong assumption, namely, there is an omniscient daemon that is able to coordinate the robots movements at each round of the synchronous system. Interestingly, this upper bound is related to the topology of the graph. More precisely, the paper associates with each graph a labeled tree that captures the paths that have to be traversed by a single robot at a time (as if they were a simple edge). The length of the longest of these labeled paths reveals to be the key parameter to determine the upper bound k on the number of robots.