A Wait-Free Stack

Abstract

In this paper, we describe a novel algorithm to create a concurrent wait-free stack. To the best of our knowledge, this is the first wait-free algorithm for a general purpose stack. In the past, researchers have proposed restricted wait-free implementations of stacks, lock-free implementations, and efficient universal constructions that can support wait-free stacks. The crux of our wait-free implementation is a fast pop operation that does not modify the stack top; instead, it walks down the stack till it finds a node that is unmarked. It marks it but does not delete it. Subsequently, it is lazily deleted by a cleanup operation. This operation keeps the size of the stack in check by not allowing the size of the stack to increase beyond a factor of W as compared to the actual size. All our operations are wait-free and linearizable.

Concurrent Fixed-Size Allocation and Free in Constant Time

“…We chose to start with the P-SIM stack because it naturally satsifies most of the properties we are aiming for. Some alternatives include Kogan and Petrank's wait-free queue [19], Ramalhete and Correia's waitfree queue [26] and Goel, Aggarwal and Sarangi's wait-free stack [13]. The first alternative requires unbounded sequence numbers and it is not clear how to get rid of them, and the latter two require Ω(p) time per operation.…”

“…With wait-free memory reclamation, the memory allocation part becomes the new limiting factor, which motivates the need for wait-free dynamic memory allocation. Applications of our memory allocation result include wait-free universal constructions ( [9,15] to name a few), wait-free queues [26,19] and wait-free stacks [13].…”