Lock-free dynamic hash tables with open addressing

TL;DR

This paper introduces a lock-free hash table algorithm with open addressing that guarantees bounded operation completion, performs efficiently on both single and multiprocessor systems, and is verified using formal methods.

Contribution

It presents a novel lock-free hash table algorithm with formal correctness proofs, improving robustness and performance over traditional lock-based methods.

Findings

Constant-time average operations for insertion, deletion, and access.

Efficient scalability with growing and shrinking hash tables.

Formal verification of 200 invariance properties using PVS.

Abstract

We present an efficient lock-free algorithm for parallel accessible hash tables with open addressing, which promises more robust performance and reliability than conventional lock-based implementations. ``Lock-free'' means that it is guaranteed that always at least one process completes its operation within a bounded number of steps. For a single processor architecture our solution is as efficient as sequential hash tables. On a multiprocessor architecture this is also the case when all processors have comparable speeds. The algorithm allows processors that have widely different speeds or come to a halt. It can easily be implemented using C-like languages and requires on average only constant time for insertion, deletion or accessing of elements. The algorithm allows the hash tables to grow and shrink when needed. Lock-free algorithms are hard to design correctly, even when apparently straightforward. Ensuring the correctness of the design at the earliest possible stage is a major challenge in any responsible system development. In view of the complexity of the algorithm, we turned to the interactive theorem prover PVS for mechanical support. We employ standard deductive verification techniques to prove around 200 invariance properties of our algorithm, and describe how this is achieved with the theorem prover PVS.