Abstract: Reduction algorithms are used widely in parallel computing.There are many reduction algorithms applied to different situations.These reduction algorithms are different from each other.Logical topology is the key cause to make the differences.In order to unify the description of reduction algorithms,and uncover their common feature,a definition of logical topology and its properties were presented in this paper.Based on it,a unified description for reduction algorithms was proposed.The description contributes to understand reduction algorithms and thus to design efficient reduction algorithms for different computational applications and environments.It can also be regarded as a reduction algorithmic framework for integrating different semantics and thus maybe guide to design new reduction algorithms with the semantics.Essentially,the unified description is a definition of reduction algorithms formally,and so it helps to verify correctness of reduction algorithms.

Key words: Reduction algorithm,Logic topology,Algorithm description,Parallel computing