An $\Omega(n \log n)$ Lower Bound on the Cost of Mutual Exclusion

Abstract

We prove an $\Omega(n \log n)$ lower bound on the number ofnon-busywaiting memory accesses by any deterministic algorithm solving$n$ process mutual exclusion that communicates via shared registers.The cost of the algorithm is measured in the \emph{state change} costmodel, a variation of the cache coherent model. Our bound is tight inthis model. We introduce a novel information theoretic prooftechnique. We first establish a lower bound on the information neededby processes to solve mutual exclusion. Then we relate the amount ofinformation processes can acquire through shared memory accesses tothe cost they incur. We believe our proof technique is flexible andintuitive, and may be applied to a variety of other problems andsystem models.