Space-Efficient Lock-Free Linear-Probing Hash Table

2026-06-15

AI Summary

This work addresses the challenge of achieving strong liveness properties—such as lock-freedom and wait-free lookups—in highly concurrent settings while preserving the space efficiency of linear probing hash tables. We present the first lock-free concurrent linear probing hash table that incurs only a minimal metadata overhead per entry, requiring merely a constant or logarithmic number of additional bits. By leveraging lightweight metadata, atomic primitives such as LL/SC or CAS, and amortized analysis, our design supports linearizable operations and safe memory reclamation. Under the assumption of no duplicate keys in concurrent insertions, the expected amortized step complexity of insertions, deletions, and lookups matches that of the sequential variant, thereby combining compact memory layout with high concurrency performance.

Abstract

Linear probing is one of the simplest and most space-efficient approaches to hash table design, and is widely used in sequential settings due to its compact memory layout. However, designing a concurrent linear-probing hash table with strong liveness guarantees has proved difficult, and only a handful of such algorithms have been proposed, all of which either restrict concurrency or rely on large per-entry metadata, thereby compromising space efficiency. We present a lock-free linear-probing hash table with wait-free lookups that retains the core advantages of sequential linear probing while handling contention gracefully. Our design uses only a small amount of metadata per table entry: a constant number of additional bits when using LL/SC, or a logarithmic number of bits when using CAS. The algorithm is linearizable and lock-free, supports insert, delete, and wait-free lookup operations, and is able to safely reclaim space used by deleted elements without rebuilding the table. We analyze the amortized step complexity of our hash table assuming no concurrent insertions of the same key, and show that each operation has expected amortized step complexity matching that of sequential linear probing, up to the point contention per key.

Problem

• lock-free
• linear-probing
• hash table
• space-efficient
• concurrent

Innovation

• lock-free
• linear probing
• space-efficient
• wait-free lookup
• linearizable