Space-efficient FCFS group mutual exclusion

Hadzilacos in [Proc. 20th Annual Symp. on Principles of Distributed Computing, 2001, pp. 100-106] first introduced a fairness condition, called first-come-first-served (FCFS), for group mutual exclusion. The only known FCFS group mutual exclusion algorithm is due to Hadzilacos [Proc. 20th Annual Symp. on Principles of Distributed Computing, 2001, pp. 100-106], and requires Θ(N2) bounded shared registers, where N is the number of processes. We present a FCFS group mutual exclusion algorithm that uses only Θ(N) bounded shared registers. (The existence of such an algorithm was posed as an open problem by Hadzilacos.)