Regularising Transformations for Integral Dependencies
The high-level synthesis of parallel algorithms characterised by irregular data dependencies is a challenging task for algorithm designers. In this paper we show that for problems specified as systems of integral recurrence equations, a systematic derivation of regular arrays is possible. The approach combines established techniques based on the space-time mapping of regular (typically linear) data dependencies onto processor arrays, with systematic ways of regularising the data dependencies through powerful forms of localisation. The methods we present are applicable to a range of combinatorial problems, including the Knapsack problem, which we adopt as a case study.
KeywordsKnapsack Problem Index Function Data Dependence Systolic Array Index Point
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