Task graphs or dependence graphs are used in runtime systems to schedule tasks for parallel execution. In problem domains such as dense linear algebra and signal processing, dependence graphs can be generated from a program by static analysis. However, in emerging problem domains such as graph analytics, the set of tasks and dependences between tasks in a program are complex functions of runtime values and cannot be determined statically. In this paper, we introduce a novel approach for exploiting parallelism in such programs. This approach is based on a data structure called the kinetic dependence graph (KDG), which consists of a dependence graph together with update rules that incrementally update the graph to reflect changes in the dependence structure whenever a task is completed.

Graph algorithms are becoming increasingly important for analyzing large datasets in many fields. Real-world graph data follows a pattern of sparsity, that is not uniform but highly skewed towards a few items. Implementing graph traversal, statistics and machine learning algorithms on such data in a scalable manner is quite challenging. As a result, several graph analytics frameworks (GraphLab, CombBLAS, Giraph, SociaLite and Galois among others) have been developed, each offering a solution with different programming models and targeted at different users. Unfortunately, the "Ninja performance gap" between optimized code and most of these frameworks is very large (2-30X for most frameworks and up to 560X for Giraph) for common graph algorithms, and moreover varies widely with algorithms. This makes the end-users' choice of graph framework dependent not only on ease of use but also on performance. In this work, we offer a quantitative roadmap for improving the performance of all these frameworks and bridging the "ninja gap". We first present hand-optimized baselines that get performance close to hardware limits and higher than any published performance figure for these graph algorithms. We characterize the performance of both this native implementation as well as popular graph frameworks on a variety of algorithms. This study helps end-users delineate bottlenecks arising from the algorithms themselves vs. programming model abstractions vs. the framework implementations. Further, by analyzing the system-level behavior of these frameworks, we obtain bottlenecks that are agnostic to specific algorithms. We recommend changes to alleviate these bottlenecks (and implement some of them) and reduce the performance gap with respect to native code. These changes will enable end-users to choose frameworks based mostly on ease of use.

Asynchronous variational integrators (AVIs) are used in computational mechanics and graphics to solve complex contact mechanics problems. The parallelization of AVI is difficult problem because it is not possible to build a dependence graph for AVI either at compile-time or at runtime. However, we show that if the dependence graph for AVI can be updated incrementally as the computation is performed, it is possible to parallelize AVI in a systematic way. Using this approach, we are able to obtain speedups of up to 20 on 24 cores for relatively small AVI problems.

For more than thirty years, the parallel programming community has used the dependence graph as the main abstraction for reasoning about and exploiting parallelism in "regular" algorithms that use dense arrays, such as finite-differences and FFTs. In this paper, we argue that the dependence graph is not a suitable abstraction for algorithms in new application areas like machine learning and network analysis in which the key data structures are "irregular" data structures like graphs, trees, and sets.

Outside of computational science, most problems are formulated in terms of irregular data structures such as graphs, trees and sets. Unfortunately, we understand relatively little about the structure of parallelism and locality in irregular algorithms. In this paper, we study multiple algorithms for four such problems: discrete-event simulation, single-source shortest path, breadth-first search, and minimal spanning trees. We show that the algorithms can be classified into two categories that we call unordered and ordered, and demonstrate experimentally that there is a trade-off between parallelism and work efficiency: unordered algorithms usually have more parallelism than their ordered counterparts for the same problem, but they may also perform more work. Nevertheless, our experimental results show that unordered algorithms typically lead to more scalable implementations, demonstrating that less work-efficient irregular algorithms may be better for parallel execution.

We describe and evaluate ordered and unordered algorithms for shared-memory parallel breadth-first search. The unordered algorithm is based on viewing breadth-first search as a fixpoint computation, and in general, it may perform more work than the ordered algorithms while requiring less global synchronization.

Irregular algorithms are organized around pointer-based data structures such as graphs and trees, and they are ubiquitous in applications. Recent work by the Galois project has provided a systematic approach for parallelizing irregular applications based on the idea of optimistic or speculative execution of programs. However, the overhead of optimistic parallel execution can be substantial. In this paper, we show that many irregular algorithms have structure that can be exploited and present three key optimizations that take advantage of algorithmic structure to reduce speculative overheads. We describe the implementation of these optimizations in the Galois system and present experimental results to demonstrate their benefits. To the best of our knowledge, this is the first system to exploit algorithmic structure to optimize the execution of irregular programs.