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3.2 Speed results

Figure 3 details the CPU time9 required for each of the sample data files, as a function of the number of data points in the data file. These results are consistent with the analysis given in Section 4.1, where the algorithm appears to have a time complexity constant of approximately 0.0055, i.e. time complexity \( 0.0055n\lg n \).

Figure 3: The CPU time taken to run the program. Horizontal axis is dataset size in kilobytes, vertical axis is CPU time in seconds.

Despite the lack of speed results for an exact image enhancement algorithm, we are confident that the speeds obtained here are promising and reflect the anticipated speed increases as outlined in Section 2.1. Exact image enhancement algorithms require at best exponential time (that is, for \( n \) inputs, time of the order of \( e^{n} \)) and as evidenced here, our algorithm performs substantially better than exponential time.

Kevin Pulo