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

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

Faster Mutation Analysis via Equivalence Modulo States

Mutation analysis has many applications, such as asserting the quality of test suites and localizing faults. One important bottleneck of mutation analysis is scalability. The latest work explores the possibility of reducing the redundant execution via split-stream execution. However, split-stream execution is only able to remove redundant execution before the first mutated statement. In this paper we try to also reduce some of the redundant execution after the execution of the first mutated statement. We observe that, although many mutated statements are not equivalent, the execution result of those mutated statements may still be equivalent to the result of the original statement. In other words, the statements are equivalent modulo the current state. In this paper we propose a fast mutation analysis approach, AccMut. AccMut automatically detects the equivalence modulo states among a statement and its mutations, then groups the statements into equivalence classes modulo states, and uses only one process to represent each class. In this way, we can significantly reduce the number of split processes. Our experiments show that our approach can further accelerate mutation analysis on top of split-stream execution with a speedup of 2.56x on average.Comment: Submitted to conferenc

Equivalence Classes and Conditional Hardness in Massively Parallel Computations

The Massively Parallel Computation (MPC) model serves as a common abstraction of many modern large-scale data processing frameworks, and has been receiving increasingly more attention over the past few years, especially in the context of classical graph problems. So far, the only way to argue lower bounds for this model is to condition on conjectures about the hardness of some specific problems, such as graph connectivity on promise graphs that are either one cycle or two cycles, usually called the one cycle vs. two cycles problem. This is unlike the traditional arguments based on conjectures about complexity classes (e.g., P ? NP), which are often more robust in the sense that refuting them would lead to groundbreaking algorithms for a whole bunch of problems. In this paper we present connections between problems and classes of problems that allow the latter type of arguments. These connections concern the class of problems solvable in a sublogarithmic amount of rounds in the MPC model, denoted by MPC(o(log N)), and some standard classes concerning space complexity, namely L and NL, and suggest conjectures that are robust in the sense that refuting them would lead to many surprisingly fast new algorithms in the MPC model. We also obtain new conditional lower bounds, and prove new reductions and equivalences between problems in the MPC model

Tiramisu: A Polyhedral Compiler for Expressing Fast and Portable Code

This paper introduces Tiramisu, a polyhedral framework designed to generate high performance code for multiple platforms including multicores, GPUs, and distributed machines. Tiramisu introduces a scheduling language with novel extensions to explicitly manage the complexities that arise when targeting these systems. The framework is designed for the areas of image processing, stencils, linear algebra and deep learning. Tiramisu has two main features: it relies on a flexible representation based on the polyhedral model and it has a rich scheduling language allowing fine-grained control of optimizations. Tiramisu uses a four-level intermediate representation that allows full separation between the algorithms, loop transformations, data layouts, and communication. This separation simplifies targeting multiple hardware architectures with the same algorithm. We evaluate Tiramisu by writing a set of image processing, deep learning, and linear algebra benchmarks and compare them with state-of-the-art compilers and hand-tuned libraries. We show that Tiramisu matches or outperforms existing compilers and libraries on different hardware architectures, including multicore CPUs, GPUs, and distributed machines.Comment: arXiv admin note: substantial text overlap with arXiv:1803.0041