Beyond 0-1: The 1-N Principle and Fast Validation of N-sorter Sorting Networks

The well-known 0-1 principle for traditional data-oblivious sorting networks states that a network with L inputs can be fully validated an input vector set consisting of all 2 L unique vectors containing only the values 0 and 1 in each vector’s inputs. Researchers providing proofs this tend to ignore fact, which is emphasized here, provide distinct orderings two 2-sorters perform operations networks. authors have recently described single-stage N-sorters, N >2, multiway merge use these N-sorters. new N-sorters their are also data-oblivious. It easily shown not sufficient verify even 3-sorter, smallest such N-sorter, as unable produce 3 In order propose 1-N principle, testing N-sorter N necessary prove N-sorter’s correctness. An algorithm defined generates inputs, then used associated N-sorter. validate authors’ L-input methods been created validation sets dramatically reduced size versus unsorted they derived from. For example, ratios number L! permutation equivalent >1,000,000 L=12, much higher increases.