Space Efficient Breadth-First and Level Traversals of Consistent Global States of Parallel Programs

TL;DR

This paper introduces a space-efficient algorithm for enumerating consistent global states in parallel programs, significantly reducing memory usage from exponential to polynomial space, and demonstrating practical improvements over traditional methods.

Contribution

The paper presents the first polynomial space algorithm for BFS enumeration of global states, outperforming traditional exponential space methods in both memory and speed.

Findings

Traditional BFS can exhaust JVM heap space in benchmarks.

Proposed algorithm uses less than 60 MB memory in experiments.

Algorithm is faster than traditional BFS in many cases.

Abstract

Enumerating consistent global states of a computation is a fundamental problem in parallel computing with applications to debug- ging, testing and runtime verification of parallel programs. Breadth-first search (BFS) enumeration is especially useful for these applications as it finds an erroneous consistent global state with the least number of events possible. The total number of executed events in a global state is called its rank. BFS also allows enumeration of all global states of a given rank or within a range of ranks. If a computation on n processes has m events per process on average, then the traditional BFS (Cooper-Marzullo and its variants) requires $\mathcal{O}(\frac{m^{n-1}}{n})$ space in the worst case, whereas ou r algorithm performs the BFS requires $\mathcal{O}(m^2n^2)$ space. Thus, we reduce the space complexity for BFS enumeration of consistent global states exponentially. and give the first polynomial space algorithm for this task. In our experimental evaluation of seven benchmarks, traditional BFS fails in many cases by exhausting the 2 GB heap space allowed to the JVM. In contrast, our implementation uses less than 60 MB memory and is also faster in many cases.