Reading many variables in one atomic operation: solutions with linear or sublinear complexity

We address the problem of reading several variables (components) X ₁,...,X_c, all in one atomic operation, by only one process, called the reader, while each of these variables are being written by a set of writers. All operations (i.e., both reads and writes) are assumed to be totally asynchronous and wait-free. For this problem, only algorithms that require at best quadratic time and space complexity can be derived from the existing literature. (The time complexity of a construction is the number of suboperations of a high-level operation and its space complexity is the number of atomic shared variables it needs) In this paper, we provide a deterministic protocol that has linear (in the number of processes) space complexity, linear time complexity for a read operation, and constant time complexity for a write. Our solution does not make use of time-stamps. Rather, it is the memory location where a write writes that differentiates it from the other writes. Also, introducing randomness in the location where the reader gets the value that it returns, we get a conceptually very simple probabilistic algorithm. This algorithm has an overwhelmingly small, controllable probability of error. Its space complexity, and also the time complexity of a read operation, are sublinear. The time complexity of a write is constant. On the other hand, under the Archimedean time assumption, we get a protocol whose time and space complexity do not depend on the number of writers, but are linear in the number of components only. (The time complexity of a write operation is still constant.)