Tiled Linear Algebra a System for Parallel Graph Algorithms

High performance parallel kernels for solving graph problems are complex and difficult to write. Some systems have been developed to facilitate the implementation of these kernels but the code they produce does not always perform as well as custom software. In this space, we propose Tiled Linear Algebra (TLA), a multi-level system based on linear algebra but with explicit parallel extensions. Programs can be first written in a conventional manner using linear algebra and then tuned for parallel performance using our extension. This separation allows programmers with different expertise to focus on their strengths with writing original codes that can then be tuned by parallel experts. This paper presents the background on using linear algebra to express graph algorithms and describes the extensions TLA provides to implement their parallel versions. The key extensions supported by TLA are: data distribution, partial computation, delaying updates, and communication. With these extensions to the traditional linear algebra operators, we could produce linear algebra based versions of several problems including single source shortest path that should preform close to custom implementations. We present results on several single source shortest path algorithms to demonstrate the features of TLA.