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Characterizations of Classes of Graphs Recognizable by Local Computations

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Abstract

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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Authors and Affiliations

  1. LIF, Université de Provence, 39 rue Joliot-Curie, 13453 Marseille cedex 13, France

    Emmanuel Godard

  2. LaBRI, Université Bordeaux I, ENSEIRB, 351 cours de la Libération, 33405 Talence, France

    Yves Métivier

  3. LIAFA, Université Paris VII, 2 place Jussieu, case 7014, 75251 Paris cedex 05, France

    Anca Muscholl

Authors
  1. Emmanuel Godard
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  2. Yves Métivier
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  3. Anca Muscholl
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Corresponding authors

Correspondence to Emmanuel Godard, Yves Métivier or Anca Muscholl.

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Godard, E., Métivier, Y. & Muscholl, A. Characterizations of Classes of Graphs Recognizable by Local Computations. Theory Comput Systems 37, 249–293 (2004). https://doi.org/10.1007/s00224-003-1062-1

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  • DOI: https://doi.org/10.1007/s00224-003-1062-1

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