Abstract. In this paper we present GPU-Quicksort, an efficient Quicksort algorithm suitable for highly parallel multi-core graphics processors. Quicksort has previously been considered as an inefficient sorting solution for graphics processors, but we show that GPU-Quicksort often performs better than the fastest known sorting implementations for graphics processors, such as radix and bitonic sort. Quicksort can thus be seen as a viable alternative for sorting large quantities of data on graphics processors.

In this paper we take a look at GPU-Quicksort, an efficient Quicksort algorithm suitable for the highly parallel multi-core graphics processors. Quicksort had previously been considered an inefficient sorting solution for graphics processors, but GPU-Quicksort often performs better than the fastest known sorting implementations for graphics processors, such as radix and bitonic sort. Quicksort can thus be seen as a viable alternative for sorting large quantities of data on graphics processors. We also take look at a comparison of different load balancing schemes. To get maximum performance on the many-core graphics processors it is important to have an even balance of the workload so that all processing units contribute equally to the task at hand. This can be hard to achieve when the cost of a task is not known beforehand and when new sub-tasks are created dynamically during execution. With the recent advent of scatter operations and atomic hardware primitives it is now possible to bring some of the more elaborate dynamic load balancing schemes from the conventional SMP systems domain to the graphics processor domain.

Many task-parallel applications can benefit from attempting to execute tasks in a specific order, as for instance indicated by priorities associated with the tasks. We present three lock-free data structures for priority scheduling with different trade-offs on scalability and ordering guarantees. First we propose a basic extension to work-stealing that provides good scalability, but cannot provide any guarantees for task-ordering in-between threads. Next, we present a centralized priority data structure based on k-fifo queues, which provides strong (but still relaxed with regard to a sequential specification) guarantees. The parameter k allows to dynamically configure the trade-off between scalability and the required ordering guarantee. Third, and finally, we combine both data structures into a hybrid, k-priority data structure, which provides scalability similar to the work-stealing based approach for larger k, while giving strong ordering guarantees for smaller k. We argue for using the hybrid data structure as the best compromise for generic, priority-based task-scheduling.We analyze the behavior and trade-offs of our data structures in the context of a simple parallelization of Dijkstra's single-source shortest path algorithm. Our theoretical analysis and simulations show that both the centralized and the hybrid k-priority based data structures can give strong guarantees on the useful work performed by the parallel Dijkstra algorithm. We support our results with experimental evidence on an 80-core Intel Xeon system.

We present three lock-free data structures for priority task scheduling: a priority work-stealing one, a centralized one with ρ-relaxed semantics, and a hybrid one combining both concepts. With the single-source shortest path (SSSP) problem as example, we show how the different approaches affect the prioritization and provide upper bounds on the number of examined nodes. We argue that priority task scheduling allows for an intuitive and easy way to parallelize the SSSP problem, notoriously a hard task. Experimental evidence supports the good scalability of the resulting algorithm.The larger aim of this work is to understand the trade-offs between scalability and priority guarantees in task scheduling systems. We show that ρ-relaxation is a valuable technique for improving the first, while still allowing semantic constraints to be satisfied: the lock-free, hybrid k-priority data structure can scale as well as work-stealing, while still providing strong priority scheduling guarantees, which depend on the parameter k. Our theoretical results open up possibilities for even more scalable data structures by adopting a weaker form of ρ-relaxation, which still enables the semantic constraints to be respected.

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Work-stealing systems are typically oblivious to the nature of the tasks they are scheduling. They do not know or take into account how long a task will take to execute or how many subtasks it will spawn. Moreover, task execution order is typically determined by an underlying task storage data structure, and cannot be changed. There are thus possibilities for optimizing task parallel executions by providing information on specific tasks and their preferred execution order to the scheduling system. We investigate generalizations of work-stealing and introduce a framework enabling applications to dynamically provide hints on the nature of specific tasks using scheduling strategies . Strategies can be used to independently control both local task execution and steal order. Strategies allow optimizations on specific tasks, in contrast to more conventional scheduling policies that are typically global in scope. Strategies are composable and allow different, specific scheduling choices for different parts of an application simultaneously. We have implemented a work-stealing system based on our strategy framework. A series of benchmarks demonstrates beneficial effects that can be achieved with scheduling strategies.

Abstract. In this paper we revisit the design of concurrent data structures -specifically queues -and examine their performance portability with regard to the move from conventional CPUs to graphics processors. We have looked at both lock-based and lock-free algorithms and have, for comparison, implemented and optimized the same algorithms on both graphics processors and multi-core CPUs. Particular interest has been paid to study the difference between the old Tesla and the new Fermi and Kepler architectures in this context. We provide a comprehensive evaluation and analysis of our implementations on all examined platforms. Our results indicate that the queues are in general performance portable, but that platform specific optimizations are possible to increase performance. The Fermi and Kepler GPUs, with optimized atomic operations, are observed to provide excellent scalability for both lock-based and lock-free queues.

In this article, we describe GPU-Quicksort, an efficient Quicksort algorithm suitable for highly parallel multicore graphics processors. Quicksort has previously been considered an inefficient sorting solution for graphics processors, but we show that in CUDA, NVIDIA's programing platform for general-purpose computations on graphical processors, GPU-Quicksort performs better than the fastest-known sorting implementations for graphics processors, such as radix and bitonic sort. Quicksort can thus be seen as a viable alternative for sorting large quantities of data on graphics processors.