Race Detection and Reachability in Nearly Series-Parallel DAGs.

A program is said to have a determinacy race if logically parallel parts of a program access the same memory location and one of the accesses is a write. These races are generally bugs in the program since they lead to non-deterministic program behavior --- different schedules of the program can lead to different results. Most prior work on detecting these races focuses on a subclass of programs with series-parallel or nested parallelism. This paper presents a race-detection algorithm for detecting races in a more general class of programs, namely programs that include arbitrary ordering constraints in additional to the series-parallel constructs. The algorithm performs a serial execution of the program, augmented to detect races, in O(T1 + k2) time, where T1 is the sequential running time of the original program and k is the number of non series-parallel constraints. The main technical novelty of this paper is a new data structure, R-Sketch, for answering reachability queries in nearly series-parallel (SP) directed acyclic graphs (DAGs). Given as input a graph comprising an n-node series parallel graph and k additional non-SP edges, the total construction time of the data structure is O(n + k2), and each reachability query can be answered in O(1) time. The data structure is traversally incremental, meaning that it supports the insertion of nodes/edges, but only as they are discovered through a graph traversal.