Space-efficient FCFS group mutual exclusion

In the group mutual exclusion problem [Y. Joung, Asynchronous group mutual exclusion, Distrib. Comput. 13 (2000) 189], which generalizes mutual exclusion [E. Dijkstra, Solution of a problem in concurrent programming control, Comm. ACM 8 (9) (1965) 569], a process chooses a session when it requests entry into the Critical Section. A group mutual exclusion algorithm must ensure that the mutual exclusion property holds: if two processes are in the Critical Section at the same time, then they request the same session. In addition to mutual exclusion, lockout freedom, bounded exit, and concurrent entering are basic properties that are desirable in any group mutual exclusion algorithm.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.)