Characterizations of Classes of Graphs Recognizable by Local Computations
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This paper investigates the power of local computations on graphs, by considering a classical problem in distributed algorithms, the recognition problem. Formally, we want to compute some topological information on a network of processes, possibly using additional knowledge about the structure of the underlying graph. We propose the notion of recognition with structural knowledge by means of local computations. Then we characterize the graph classes that are recognizable with or without structural knowledge. The characterizations use graph coverings and a distributed enumeration algorithm proposed by A. Mazurkiewicz. Several applications are presented, in particular concerning minor-closed classes of graphs.
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