Tarjan's famous linear time, sequential algorithm for finding the strongly connected components (SCCs) of a graph relies on depth first search, which is inherently sequential. Deterministic parallel algorithms solve this problem in logarithmic time using matrix multiplication techniques, but matrix multiplication requires a large amount of total work. Randomized algorithms based on reachability -- the ability to get from one vertex to another along a directed path -- greatly improve the work bound in the average case. However, these algorithms do not always perform well; for instance, Divide-and-Conquer Strong Components (DCSC), a scalable, divide-and-conquer algorithm, has good expected theoretical limits, but can perform very poorly on graphs for which the maximum reachability of any vertex is small. A related algorithm, MultiPivot, gives very high probability guarantees on the total amount of work for all graphs, but this improvement introduces an overhead that increases the average running time. This work introduces SCCMulti, a multi-pivot improvement of DCSC that offers the same consistency as MultiPivot without the time overhead. We provide experimental results demonstrating SCCMulti's scalability; these results also show that SCCMulti is more consistent than DCSC and is always faster than MultiPivot.

The Standard Template Adaptive Parallel Library (STAPL) is a parallel programming infrastructure that extends C++ with support for parallelism. It includes a collection of distributed data structures called pContainers that are thread-safe, concurrent objects, i.e., shared objects that provide parallel methods that can be invoked concurrently. In this work, we present the STAPL Parallel Container Framework (PCF), that is designed to facilitate the development of generic parallel containers. We introduce a set of concepts and a methodology for assembling a pContainer from existing sequential or parallel containers, without requiring the programmer to deal with concurrency or data distribution issues. The PCF provides a large number of basic parallel data structures (e.g., pArray, pList, pVector, pMatrix, pGraph, pMap, pSet). The PCF provides a class hierarchy and a composition mechanism that allows users to extend and customize the current container base for improved application expressivity and performance. We evaluate STAPL pContainer performance on a CRAY XT4 massively parallel system and show that pContainer methods, generic pAlgorithms, and different applications provide good scalability on more than 16,000 processors.

The Standard Template Adaptive Parallel Library (stapl) is a high-productivity parallel programming framework that extends C++ and stl with unified support for shared and distributed memory parallelism. stapl provides distributed data structures (pContainers) and parallel algorithms (pAlgorithms) and a generic methodology for extending them to provide customized functionality. The stapl runtime system provides the abstraction for communication and program execution. In this paper, we describe the major components of stapl and present performance results for both algorithms and data structures showing scalability up to tens of thousands of processors.