How robust are average complexity measures? A statistical case study

Average case analysis forms an interesting and intriguing part of algorithm theory since it explains why some algorithms with bad worst-case complexity can better themselves in performance on the average. Well known examples include the quicksort, simplex method and the wide variety of computer graphics and computational geometry algorithms. Here we make a statistical case study of the robustness of average complexity measures, which are derived assuming uniform distribution, for non-uniform inputs (both discrete and continuous).