New Concurrent Order Maintenance Data Structure

TL;DR

This paper introduces a parallel order-maintenance data structure that significantly improves the speed of comparisons and updates on large ordered lists, leveraging lock-free techniques for comparisons and lock-based synchronization for updates.

Contribution

It presents a novel parallel OM data structure with lock-free comparisons and lock-based insertions/deletions, achieving substantial speedups on multicore systems.

Findings

Lock-free comparisons achieve up to 34.4x speedup with 64 workers.

Lock-based insertions and deletions achieve up to 7x and 5.6x speedups respectively.

The approach is highly effective for applications with many more comparisons than updates.

Abstract

The \emph{Order-Maintenance} (OM) data structure maintains a total order list of items for insertions, deletions, and comparisons. As a basic data structure, OM has many applications, such as maintaining the topological order, core numbers, and truss in graphs, and maintaining ordered sets in Unified Modeling Language (UML) Specification. The prevalence of multicore machines suggests parallelizing such a basic data structure. This paper proposes a new parallel OM data structure that supports insertions, deletions, and comparisons in parallel. Specifically, parallel insertions and deletions are synchronized by using locks efficiently, which achieve up to $7$x and $5.6$x speedups with $64$ workers. One big advantage is that the comparisons are lock-free so that they can execute highly in parallel with other insertions and deletions, which achieve up to $34.4$x speedups with $64$ workers. Typical real applications maintain order lists that always have a much larger portion of comparisons than insertions and deletions. For example, in core maintenance, the number of comparisons is up to 297 times larger compared with insertions and deletions in certain graphs. This is why the lock-free order comparison is a breakthrough in practice.