An Asynchronous Message-passing Distributed Algorithm for the Generalized Local Critical Section Problem

This paper discusses the generalized local version of critical section problems including mutual exclusion, mutual inclusion, k-mutual exclusion and l-mutual inclusion. When a pair of numbers (li, ki) is given for each process Pi, it is the problem of controlling the system in such a way that the number of processes which can be execute their critical sections at a time is at least li and at most ki among its neighboring processes and Pi itself. First, we show the relationship between the generalized local (li, ki)-critical section problem and the generalized local (|Ni| + 1-ki, |Ni| + 1 - li) -critical section problem. Next, we propose the first solution for the generalized local (li, ki)-critical section problem for arbitrary (li, ki), where 0 < li < ki < |Ni| + 1 for each process Pi.