SIAM Journal on Control and Optimization
Gathering of asynchronous robots with limited visibility
Theoretical Computer Science
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Gathering asynchronous oblivious mobile robots in a ring
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Taking advantage of symmetries: Gathering of many asynchronous oblivious robots on a ring
Theoretical Computer Science
How to meet asynchronously (almost) everywhere
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Rendezvous of mobile agents without agreement on local orientation
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Almost optimal asynchronous rendezvous in infinite multidimensional grids
DISC'10 Proceedings of the 24th international conference on Distributed computing
Exclusive perpetual ring exploration without chirality
DISC'10 Proceedings of the 24th international conference on Distributed computing
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 new approach for analyzing convergence algorithms for mobile robots
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
Gathering of six robots on anonymous symmetric rings
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
Optimal probabilistic ring exploration by semi-synchronous oblivious robots
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
Mobile robots gathering algorithm with local weak multiplicity in rings
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
How to gather asynchronous oblivious robots on anonymous rings
DISC'12 Proceedings of the 26th international conference on Distributed Computing
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The paper studies the gathering problem on grid networks. A team of robots placed at different nodes of a grid, have to meet at some node and remain there. Robots operate in Look-Compute-Move cycles; in one cycle, a robot perceives the current configuration in terms of occupied nodes (Look), decides whether to move towards one of its neighbors (Compute), and in the positive case makes the computed move instantaneously (Move). Cycles are performed asynchronously for each robot. The problem has been deeply studied for the case of ring networks. However, the known techniques used on rings cannot be directly extended to grids. Moreover, on rings, another assumption concerning the so-called multiplicity detection capability was required in order to accomplish the gathering task. That is, a robot is able to detect during its Look operation whether a node is empty, or occupied by one robot, or occupied by an undefined number of robots greater than one. In this paper, we provide a full characterization about gatherable configurations for grids. In particular, we show that in this case, the multiplicity detection is not required. Very interestingly, sometimes the problem appears trivial, as it is for the case of grids with both odd sides, while sometimes the involved techniques require new insights with respect to the well-studied ring case. Moreover, our results reveal the importance of a structure like the grid that allows to overcome the multiplicity detection with respect to the ring case.