Long-lived, fast, waitfree renaming with optimal name space and high throughput

Abstract

The (n, k, l)-renaming problem requires that names from the set {1,..., l} are assigned to processes from a set of size n, provided that no more than k ≤ l processes axe simultaneously either holding or trying to acquire a name. A solution to this problem supplies a renaming object supporting both acquire and release operations so that no two processes ever simultaneously hold the same name. The protocol is waitfree if each participant successfully completes either operation in a bounded number of its own steps regardless of the speed of other processes; it is long-lived if it there is no bound on the number of operations that can be applied to the object; it is fast if the number of steps taken by any process before it completes an operation is independent of n; and it is name-space-optimal if l = k.

This paper presents the first renaming algorithm for atomic read/write registers that is waitfree, long-lived, fast, and name-space-optimal. Since optimal name space is impossible for deterministic renaming algorithms, our algorithm is randomized. The maximum number (over schedulers and processes) of the expected number (over coin flips) of accesses to read/write registers required to complete either an acquire or release operation is θ(k ²).

We also define a notion of amortized expected complexity that measures the throughput of a system. The amortized expected step complexity of the new renaming algorithm is θ(k log k), which is a substantial improvement, in this amortized sense, over any preceding long-lived renaming algorithm for read/write registers (whether name-space-optimal or not). The notion of amortized complexity of waitfree protocols may be of independent interest since it seems to suggest that waitfreedom may not be as impractical as is sometimes suspected.

Research was supported in part by Natural Sciences and Engineering Research Council of Canada grant OGP0089756.

Research was supported in part by Natural Sciences and Engineering Research Council of Canada grant OGP0041900.

Research was supported in part by Natural Sciences and Engineering Research Council of Canada grant dOGP0041900 and DeVry Institute of Technology, Calgary, Canada.