Group Mutual Exclusion in Linear Time and Space

Abstract

The Group Mutual Exclusion (GME) problem, introduced by Joung, is a natural extension of the classical Mutual Exclusion problem. In the classical Mutual Exclusion problem, two or more processes are not simultaneously allowed to be in their CRITICAL SECTION, a piece of code where a common resource is accessed. In the GME problem, it is necessary to impose mutual exclusion on different groups in processes in accessing a resource, while allowing processes of the same group to share the resource. The Group Mutual Exclusion problem arises in several applications and is the focus of this thesis. We present an algorithm for the GME problem that satisfies the properties of Mutual Exclusion, Starvation Freedom, Bounded Exit, Concurrent Entry and First-Come-First Served. Our algorithm has [theta] (N) shared space complexity and [omicron] (N)RMR (Remote Memory Reference) complexity. Our algorithm is developed by generalizing the well-known Lamport's Bakery Algorithm for the classical mutual exclusion problem, while preserving its simplicity and elegance. Just like Lamport's Bakery Algorithm, our algorithm has the disadvantage that the token numbers can grow in an unbunded manner. When all shared variables are required to be of bounded size, Hadzilacos presented an algorithm, whose shared space complexity is [theta] (N²) and whose RMR complexity is claimed to be [omicron] (N). Hadzilacos posed as an open problem, the development of a linear time and space algorithm that uses only bounded shared variables and only simple read and write instructions. As a solution to the open problem, Jayanti et al. presented a space efficient adaptation of the above algorithm that uses only [theta] (N) shared space and inherited the claim that the RMR complexity is [omicron] (N) We show that both of these algorithms are of RMR complexity [omega] (N²) and thus demonstrate that both claims are erroneous. So, the open problem posed by Hadzilacos is still open.