Two novel suboptimal algorithms for mutual exclusion in distributed systems are presented. One is based on the modi cation of Maekawa's grid based quorum scheme. The size of quorums is approximately p 2 p N where N is the number of sites in a network, as compared to 2 p N of the original method. The method is simple and geometrically evident. The second one is based on the idea of di erence sets in combinatorial theory. The resulting scheme is very close to optimal in terms of quorum size.