Race Detection in Two Dimensions

Abstract

Dynamic race detection is a program analysis technique for detecting errors caused by undesired interleavings of concurrent tasks. A primary challenge when designing efficient race detection algorithms is to achieve manageable space requirements. State-of-the-art algorithms for unstructured parallelism require Θ ( n ) space per monitored memory location, where n is the total number of tasks. This is a serious drawback when analyzing programs with many tasks. In contrast, algorithms for programs with a series-parallel (SP) structure require only Θ (1) space. Unfortunately, it is currently not well understood if there are classes of parallelism beyond SP that can also benefit from and be analyzed with Θ (1) space complexity. In this work, we show that structures richer than SP graphs, namely, that of two-dimensional (2D) lattices, can also be analyzed in Θ (1) space. Toward that (a) we extend Tarjan’s algorithm for finding lowest common ancestors to handle 2D lattices; (b) from that extension we derive a serial algorithm for race detection that can analyze arbitrary task graphs with a 2D lattice structure; (c) we present a restriction to fork-join that admits precisely the 2D lattices as task graphs (e.g., it can express pipeline parallelism). Our work generalizes prior work on structured race detection and aims to provide a deeper understanding of the interplay between structured parallelism and program analysis efficiency.