On the mailbox problem

Abstract

The Mailbox Problem was described and solved by Aguilera, Gafni, and Lamport in [2] with a mailbox algorithm that uses two flag registers that carry 14 values each. An interesting question that they ask is whether leaner solutions exists. In addition to their algorithm, the authors of [2] proved that the mailbox problem cannot be solved with 1 bit flags. In this paper, we show that 2 bit flags suffice by presenting a mailbox algorithm with two bit flags. The space complexity of Aguilera et al. solution is O(n log n) and they conjectured that a solution with space complexity O(log n) exists. Our algorithm proves this conjecture. We also prove that there is no mailbox algorithm with a smaller space complexity.