Abstract
We study the multiparty communication model where players are the nodes of a graph G and each of these nodes knows his/her own identifier together with the identifiers of his/her neighbors. The nodes simultaneously send a unique message to a referee who must give the output (which is a fiunction of G). In this paper we prove that counting the numbers of connected components of G and deciding the connectivity of G are equivalent problems (in terms of the size of the messages).
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Lizama, A., Rapaport, I. (2022). Connectivity and Connected Components in the Number-in-Hand Computation Model. In: Adamatzky, A. (eds) Automata and Complexity. Emergence, Complexity and Computation, vol 42. Springer, Cham. https://doi.org/10.1007/978-3-030-92551-2_6
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DOI: https://doi.org/10.1007/978-3-030-92551-2_6
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