Speedup of Vidyasankar's algorithm for the group

Vidyasankar introduced a combined problem of k-exclusion and group mutual exclusion, called the group k-exclusion problem, which occurs in a situation where philosophers with the same interest can attend a forum in a meeting room, and up to k meeting rooms are available. We propose an improvement to Vidyasankar's algorithm. Waiting times in the trying region in the original algorithm and in our algorithm are bounded by n(n - k)c + O(n3(n - k))l and (n - k)c + O(n(n - k)2)l, respectively, where n is the number of processes, l is an upper bound on the time between successive two atomic steps, and c is an upper bound on the time that any philosopher spends in a forum.