Election in Fully Anonymous Shared Memory Systems: Tight Space Bounds and Algorithms

This article addresses election in fully anonymous systems made up of n asynchronous processes that communicate through atomic read-write registers or atomic read-modify-write registers. Given an integer d∈ { 1, ⋯, n- 1 }, two elections problems are considered: d-election (at least one and at most d processes are elected) and exact d-election (exactly d processes are elected). Full anonymity means that both the processes and the shared registers are anonymous. Memory anonymity means that the processes may disagree on the names of the shared registers. That is, the same register name A can denote different registers for different processes, and the register name A used by a process and the register name B used by another process can address the same shared register. Let n be the number of processes, m the number of atomic read-modify-write registers, and let M(n,d)={k:∀ℓ:1<ℓ≤n:gcd(ℓ,k)≤d}. The following results are presented for solving election in such an adversarial full anonymity context. It is possible to solve d-election when participation is not required if and only if m∈ M(n, d).It is possible to solve exact d-election when participation is required if and only if gcd(m, n) divides d.It is possible to solve d-election when participation is required if and only if gcd(m, n) ≤ d.Neither d-election nor exact d-election (be participation required or not) can be solved when the processes communicate through read-write registers only.