“…In terms of the maximal number of processes in a group, two classes of mutual exclusion problem are distinguished in the literature. The first class, called the basic mutual exclusion problem [2,3,4,5,6,7,8,9], where the maximum size of groups is one, and the second class called group mutual exclusion (GME) problem, where every group can have more than one process [1,10,11,12,13,14,15,16].…”