A Bridge Between the Asynchronous Message Passing Model and Local Computations in Graphs
A distributed system is a collection of processes that can interact. Three major process interaction models in distributed systems have principally been considered: – the message passing model, – the shared memory model, – the local computation model. In each model the processes are represented by vertices of a graph and the interactions are represented by edges. In the message passing model and the shared memory model, processes interact by communication primitives: messages can be sent along edges or atomic read/write operations can be performed on registers associated with edges. In the local computation model interactions are defined by labelled graph rewriting rules; supports of rules are edges or stars. These models (and their sub-models) reflect different system architectures, different levels of synchronization and different levels of abstraction. Understanding the power of various models, the role of structural network properties and the role of the initial knowledge enhances our understanding of basic distributed algorithms. This is done with some typical problems in distributed computing: election, naming, spanning tree construction, termination detection, network topology recognition, consensus, mutual exclusion. Furthermore, solutions to these problems constitute primitive building blocks for many other distributed algorithms. A survey may be found in [FR03], this survey presents some links with several parameters of the models including synchrony, communication media and randomization. An important goal in the study of these models is to understand some relationships between them. This paper is a contribution to this goal; more precisely we establish a bridge between tools and results presented in [YK96] for the message passing model and tools and results presented in [Ang80, BCG+96, Maz97, CM04, CMZ04, Cha05] for the local computation model.
KeywordsLocal Computation Label Graph Naming Algorithm Local View Election Algorithm
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- [Ang80]Angluin, D.: Local and global properties in networks of processors. In: Proceedings of the 12th Symposium on Theory of Computing, pp. 82–93 (1980)Google Scholar
- [AW98]Attiya, H., Welch, J.: Distributed computing: fundamentals, simulations, and advanced topics. McGraw-Hill, New York (1998)Google Scholar
- [BCG+96]Boldi, P., Codenotti, B., Gemmell, P., Shammah, S., Simon, J., Vigna, S.: Symmetry breaking in anonymous networks: Characterizations. In: Proc. 4th Israeli Symposium on Theory of Computing and Systems, pp. 16–26. IEEE Computer Society Press, Los Alamitos (1996)Google Scholar
- [BV99]Boldi, P., Vigna, S.: Computing anonymously with arbitrary knowledge. In: Proceedings of the 18th ACM Symposium on principles of distributed computing, pp. 181–188. ACM Press, New York (1999)Google Scholar
- [GMM04]Godard, E., Métivier, Y., Muscholl, A.: Characterization of Classes of Graphs Recognizable by Local Computations. Theory of Computing Systems (37), 249–293 (2004)Google Scholar
- [LeL77]LeLann, G.: Distributed systems: Towards a formal approach. In: Gilchrist, B. (ed.) Information processing 1977, pp. 155–160. North-Holland, Amsterdam (1977)Google Scholar
- [RFH72]Rosenstiehl, P., Fiksel, J.-R., Holliger, A.: Intelligent graphs. In: Read, R. (ed.) Graph theory and computing, pp. 219–265. Academic Press, New York (1972)Google Scholar