A New Group Quorum System of Large Degree

The group mutual exclusion problem is a generalization of the ordinary mutual exclusion problem where each applica-tion process can be a member of different groups and mem-bers of the same group are allowed simultaneous access to their critical sections. Members of different groups must access their critical sections in a mutually exclusive man-ner. Quorum-based solutions have been proposed for solv-ing the mutual exclusion problem in both settings. Recently, there has been a growing interest in designing group quorum systems for group mutual exclusion. The disadvantage of this approach is that it limits the level of concurrency (also known as degree) of any m-group quorum system (m> 1) to n, where n is the number of manager processes in the system. The advantage is that it provides a way from which truly distributed quorum-based solutions for group mutual exclusion can be easily constructed. Group quorum sys-tems of optimal degree are known only for n = p2k, where p is a prime, and k is a positive integer. The best known group quorum system that works for any n and m> 1 is due to Joung (2003) and has degree k = q 2n m(m−1). In this paper, we describe a new group quorum system of degree k ′ = 1 + p 1 + n m, which is much higher than k for m> 3. Also when k ′ = k, our system produces quorums of smaller size for m> k/2