K-Model: A New Computational Model for Stream Processors

Abstract

We introduce K-model, a computational model to evaluate the algorithms designed for graphic processors, and other architectures adhering to the stream programming model. We address the lack of a formal complexity model that properly accounts for memory contention, address coalescing in memory accesses, or the serial control of instruction flows. We study the impact of K-model rules on algorithm design. We devise a coalesced and low contention data access technique for Batcher's networks, and we evaluate the effectiveness of this technique within our K-model. To evaluate the benefits in using K-model in evaluating solutions for streaming architectures, we compare the complexity of a sorting network built using our technique, and quick sort. Although in theory quick sort is more efficient than bitonic sort, empirically, our bitonic sorting network has been shown to be faster than the state-of-the-art implementation of quick sort on graphics processing units (GPUs). We use our K-model to prove that this observation should generally hold. As a side result, our technique to perform a Batcher's network on GPUs improves the performance of one the fastest comparison-based solution for integers sorting.