Leader election problem on networks in which processor identity numbers are not distinct

In the networks considered in this paper, processors do not have distinct identity numbers. On such a network, we discuss the leader election problem and the problem of counting the number of processors having the same identity number. As the communication mode, we consider port-to-port, broadcast-to-port, port-to-mail box, and broadcast-to-mailbox. For each of the above communication modes, we present: an algorithm for counting the number of processors with the same identity number; an algorithm for solving the leader election problem; and a graph theoretical characterization of the solvable class for the leader election problem.