Tight RMR Lower Bounds for Mutual Exclusion

We investigate the remote memory references (RMRs) complexity of deterministic processes that communicate by reading and writing shared memory in asynchronous cache-coherent and distributed shared-memory multiprocessors. We define a class of algorithms that we call order encoding. By applying information-theoretic arguments, we prove that every order encoding algorithm, shared by n processes, has an execution that incurs Ω(n logn) RMRs. From this we derive the same lower bound for the mutual exclusion, bounded counter and store/collect synchronization problems. The bounds we obtain for these problems are tight. It follows from the results of [10] that our lower bounds hold also for algorithms that can use comparison primitives and loadlinked/store-conditional in addition to reads and writes. Our mutual exclusion lower bound proves a longstanding conjecture of Anderson and Kim.