Kernel Partitioning of Streaming Applications: A Statistical Approach to an NP-complete Problem

One of the greatest challenges in computer architecture is how to write efficient, portable, and correct software for multi-core processors. A promising approach is to expose more parallelism to the compiler, through the use of domain-specific languages. The compiler can then perform complex transformations that the programmer would otherwise have had to do. Many important applications related to audio and video encoding, software radio and signal processing have regular behavior that can be represented using a stream programming language. When written in such a language, a portable stream program can be automatically mapped by the stream compiler onto multicore hardware. One of the most difficult tasks of the stream compiler is partitioning the stream program into software threads. The choice of partition significantly affects performance, but finding the optimal partition is an NP-complete problem. This paper presents a method, based on Extreme Value theory (EVT), that statistically estimates the performance of the optimal partition. Knowing the optimal performance improves the evaluation of any partitioning algorithm, and it is the most important piece of information when deciding whether an existing algorithm should be enhanced. We use the method to evaluate a recently-published partitioning algorithm based on a heuristic. We further analyze how the statistical method is affected by the choice of sampling method, and we recommend how sampling should be done. Finally, since a heuristic-based algorithm may not always be available, the user may try to find a good partition by picking the best from a random sample. We analyze whether this approach is likely to find a good partition. To the best of our knowledge, this study is the first application of EVT to a graph partitioning problem.