Distributed Anonymous Mobile Robots: Formation of Geometric Patterns
SIAM Journal on Computing
Spectral Properties of Banded Toeplitz Matrices
Spectral Properties of Banded Toeplitz Matrices
Local strategies for maintaining a chain of relay stations between an explorer and a base station
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Optimal strategies for maintaining a chain of relays between an explorer and a base camp
Theoretical Computer Science
Randomized Gathering of Mobile Robots with Local-Multiplicity Detection
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
A local O(n2) gathering algorithm
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
Relay Positioning for Unmanned Aerial Vehicle Surveillance*
International Journal of Robotics Research
A tight runtime bound for synchronous gathering of autonomous robots with limited visibility
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
A continuous, local strategy for constructing a short chain of mobile robots
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
Local, self-organizing strategies for robotic formation problems
ALGOSENSORS'11 Proceedings of the 7th international conference on Algorithms for Sensor Systems, Wireless Ad Hoc Networks and Autonomous Mobile Entities
Continuous local strategies for robotic formation problems
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
Hi-index | 0.00 |
Consider two far apart base stations connected by an arbitrarily winding chain of n relay robots to transfer messages between them. Each relay acts autonomously, has a limited communication range, and knows only a small, local part of its environment. We seek a strategy for the relays to minimize the chain's length. We describe a large strategy class in form of linear transformations of the spatial vectors connecting neighboring robots. This yields surprising correlations between several strategy properties and characteristics of these transformations (e.g., "reasonable" strategies correspond to transformations given by doubly stochastic matrices). Based on these results, we give almost tight bounds on the strategies' convergence speed by applying and extending results about the mixing time of Markov chains. Eventually, our framework enables us to define strategies where each relay bases its decision where to move only on the positions of its k next left and right neighbors, and to prove a convergence speed of Θ(n2/k2 log n) for these strategies. This not only closes a gap between upper and lower runtime bounds of a known strategy (Go-To-The-Middle), but also allows for a trade-off between convergence properties and locality.