Distributed Anonymous Mobile Robots: Formation of Geometric Patterns
SIAM Journal on Computing
Gathering of asynchronous robots with limited visibility
Theoretical Computer Science
Fault-Tolerant Gathering Algorithms for Autonomous Mobile Robots
SIAM Journal on Computing
Asynchronous deterministic rendezvous in graphs
Theoretical Computer Science
Deterministic Rendezvous in Graphs
Algorithmica
Impossibility of gathering by a set of autonomous mobile robots
Theoretical Computer Science
Gathering asynchronous oblivious mobile robots in a ring
Theoretical Computer Science
Taking Advantage of Symmetries: Gathering of Asynchronous Oblivious Robots on a Ring
OPODIS '08 Proceedings of the 12th International Conference on Principles of Distributed Systems
Solving the robots gathering problem
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
How to meet asynchronously (almost) everywhere
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Polynomial deterministic rendezvous in arbitrary graphs
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Mobile robots gathering algorithm with local weak multiplicity in rings
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
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We consider the problem of gathering identical, memoryless, mobile agents in one node of an anonymous graph. Agents start from different nodes of the graph. They operate in Look-Compute-Move cycles and have to end up in the same node. In one cycle, an agent takes a snapshot of its immediate neighborhood (Look), makes a decision to stay idle or to move to one of its adjacent nodes (Compute), and in the latter case makes an instantaneous move to this neighbor (Move). Cycles are performed asynchronously for each agent. The novelty of our model with respect to the existing literature on gathering asynchronous oblivious agents in graphs is that the agents have very restricted perception capabilities: they can only see their immediate neighborhood. An initial configuration of agents is called gatherable if there exists an algorithm that gathers all the agents of the configuration in one node and keeps them idle from then on, regardless of the actions of the asynchronous adversary. (The algorithm can be even tailored to gather this specific configuration.) The gathering problem is to determine which configurations are gatherable and find a (universal) algorithm which gathers all gatherable configurations. We give a complete solution of the gathering problem for regular bipartite graphs. Our main contribution is the proof that the class of gatherable initial configurations is very small: it consists only of "stars" (an agent A with all other agents adjacent to it) of size at least 3. On the positive side we give an algorithm accomplishing gathering for every gatherable configuration.