Comments on the paper "parallel efficiency can be greater than unity"
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We are compelled to comment on the two short communications in the July 1986 issue of Parallel Computing on the same subject but with opposite viewpoints. They are entitled "Supeflinear speedup of an efficient serial algorithm is not possible" [1] and "Parallel efficiency can be greater than unity" [2]. The first c~:)mmunication was authored by us and showed that from an algorithm point of view, superlir~,ear speedup is impossible unless hardware considerations like context switching or memory size are considered. The proof that we employed was to take any algorithm that purported to have supeflinear speedup and show that by 'emulating' the parallel algorithm in a serial manner, we arrive at a sequential algorithm that is at worst P times slower than the parallel (where P is the number of processors). It is important to note that this statement is a theorem, which follows logically from two assumptions: (1) hardware considerations are ignored and (2) the definition of speedup. There are two ways in which one may argue with our theorem. One might disagree with our assumptions or one might claim our proof to be invalid. If one chooses to claim that hardware considerations cannot be ignored, then our theorem may not hold. However, in evaluating a particular parallel algorithm, it is clear that the correct definition of speedup should be
[1] Vance Faber,et al. Superlinear speedup of an efficient sequential algorithm is not possible , 1986, Parallel Comput..
[2] D. Parkinson. Parallel efficiency can be greater than unity , 1986, Parallel Comput..