A time complexity lower bound for randomized implementations of some shared objects
Prasad Jayanti · 1998
Many recent wait-free implementations are based on a sharedmemory that supports a pair of synchronization operations, known as LL and SC. In this paper, we establish an intrinsic performance limitation of these operations: even the simple wakeup problem [16], which requires some process to detect that all n processes are up, cannot be solved unless some process performs#for n) shared-memory operations. Using this basic result, we derive a#230 n) lower bound on the worst-case shared-access time complexity of n-process implementations of several types of objects, including fetch&increment, fetch&multiply, fetch&and, queue, and stack. (The worst-case shared-access time complexity of an implementation is the number of shared-memory operations that a process performs, in the worst-case, in order to complete a single operation on the implementation.) Our lower bound is strong in several ways: it holds even if (1) shared-memory has an infinite number of words, each of unbounded size, (2) sh...