Computing on Anonymous Networks: Part I-Characterizing the Solvable Cases

In anonymous networks, the processors do not have identity numbers. We investigate the following representative problems on anonymous networks: (a) the leader election problem, (b) the edge election problem, (c) the spanning tree construction problem, and (d) the topology recognition problem. On a given network, the above problems may or may not be solvable, depending on the amount of information about the attributes of the network made available to the processors. Some possibilities are: (1) no network attribute information at all is available, (2) an upper bound on the number of processors in the network is available, (3) the exact number of processors in the network is available, and (4) the topology of the network is available. In terms of a new graph property called “symmetricity,” in each of the four cases (1)–(4) above, we characterize the class of networks on which each of the four problems (a)–(d) is solvable. We then relate the symmetricity of a network to its 1and 2-factors. ∗To appear in IEEE Trans. Parallel and Distributed Computing, February, 1996. M. Yamashita is with the Department of Electrical Engineering, Hiroshima Univeristy, Higashi-Hiroshima, 724 Japan. T. Kameda is with the School of Computing Science, Simon Fraser University, Burnaby, B.C., Canada V5A 1S6. This work was supported in part by the Natural Sciences and Engineering Council of Canada and a Scientific Research Grant-in-Aid from the Ministry of Education, Science and Culture of Japan.