Group mutual exclusion in linear time and space

We present two algorithms for the Group Mutual Exclusion (GME) Problem that satisfy the properties of Mutual Exclusion, Starvation Freedom, Bounded Exit, Concurrent Entry and First Come First Served. Both our algorithms use only simple read and write instructions, have O(N) Shared Space complexity and O(N) Remote Memory Reference (RMR) complexity in the Cache Coherency (CC) model. Our first algorithm is developed by generalizing the well-known Lamport's Bakery Algorithm for the classical mutual exclusion problem, while preserving its simplicity and elegance. However, it uses unbounded shared registers. Our second algorithm uses only bounded registers and is developed by generalizing Taubenfeld's Black and White Bakery Algorithm to solve the classical mutual exclusion problem using only bounded shared registers. We show that contrary to common perception our algorithms are the first to achieve these properties with this combination of complexities.