# Using Skip Graphs for Increased NUMA Locality

## TL;DR

This paper introduces a skip graph-based data partitioning technique that significantly improves NUMA locality and reduces contention in concurrent data structures, with implementations demonstrating notable performance gains and reduced remote memory accesses.

## Contribution

The paper presents a novel skip graph partitioning method that enhances NUMA locality and contention reduction, along with implementations of maps and relaxed priority queues showing competitive performance.

## Key findings

- 6x higher CAS locality with lazy skip graphs
- 68.6% reduction in remote CAS operations
- CAS success rate increased from 88.3% to 99%

## Abstract

We present a data partitioning technique performed over skip graphs that promotes significant quantitative and qualitative improvements on NUMA locality in concurrent data structures, as well as reduced contention. We build on previous techniques of thread-local indexing and laziness, and, at a high level, our design consists of a partitioned skip graph, well-integrated with thread-local sequential maps, operating without contention. As a proof-of-concept, we implemented map and relaxed priority queue ADTs using our technique. Maps were conceived using lazy and non-lazy approaches to insertions and removals, and our implementations are shown to be competitive with state-of-the-art maps. We observe a 6x higher CAS locality, a 68.6% reduction on the number of remote CAS operations, and a increase from 88.3% to 99% CAS success rate when using a lazy skip graph as compared to a control skip list (subject to the same codebase, optimizations, and implementation practices). Qualitatively speaking, remote memory accesses are not only reduced in number, but the larger the NUMA distance between threads, the larger the reduction is. We consider two alternative implementations of relaxed priority queues that further take advantage of our data partitioning over skip graphs: (a) using ``spraying'', a well-known random-walk technique usually performed over skip lists, but now performed over skip graphs; and (b) a custom protocol that traverses the skip graph deterministically, marking elements along this traversal. We provide formal arguments indicating that the first approach is more \emph{relaxed}, that is, that the span of removed keys is larger, while the second approach has smaller contention. Experimental results indicate that the approach based on spraying performs better on skip graphs, yet both seem to scale appropriately.