Tight RMR lower bounds for mutual exclusion and other problems

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 log n) 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 load-linked/store-conditional in addition to reads and writes. Our mutual exclusion lower bound proves a longstanding conjecture of Anderson and Kim.