Computing on Anonymous Networks: Part I-Characterizing the Solvable Cases
IEEE Transactions on Parallel and Distributed Systems
Information Processing Letters
Comparison of initial conditions for distributed algorithms on anonymous networks
Proceedings of the eighteenth annual ACM symposium on Principles of distributed computing
An Efficient Algorithm for Graph Isomorphism
Journal of the ACM (JACM)
Symmetry and similarity in distributed systems
Proceedings of the fourth annual ACM symposium on Principles of distributed computing
Discrete Mathematics
An Effective Characterization of Computability in Anonymous Networks
DISC '01 Proceedings of the 15th International Conference on Distributed Computing
Local and global properties in networks of processors (Extended Abstract)
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Computing on anonymous networks with sense of direction
Theoretical Computer Science
A bridge between the asynchronous message passing model and local computations in graphs
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Computing on a partially eponymous ring
Theoretical Computer Science
Computing on a partially eponymous ring
OPODIS'06 Proceedings of the 10th international conference on Principles of Distributed Systems
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We consider a network of processors in the absence of unique identities, and study the k-Grouping problem of partitioning the processors into groups of size k and assigning a distinct identity to each group. The case k=1 corresponds to the well known problems of leader election and enumeration for which the conditions for solvability are already known. The grouping problem for k≥2 requires to break the symmetry between the processors partially, as opposed to problems like leader election or enumeration where the symmetry must be broken completely (i.e. a node has to be distinguishable from all other nodes). We determine what properties are necessary for solving these problems, characterize the classes of networks where it is possible to solve these problems, and provide a solution protocol for solving them. For the case k=2 we also consider a stronger version of the problem, called Pairing where each processor must also determine which other processor is in its group. Our results show that the solvable class of networks in this case varies greatly, depending on the type of prior knowledge about the network that is available to the processors. In each case, we characterize the classes of networks where Pairing is solvable and determine the necessary and sufficient conditions for solving the problem.