Analysis of Linear Time Sorting Algorithms

We derive CPU time formulae for the two simplest linear time-sorting algorithms, linear probing sort and bucket sort, as a function of the load factor, and show agreement with experimentally measured CPU times. This allows us to compute optimal load factors for each algorithm, whose values have previously been identified only approximately in the literature. We also present a simple model of cache latency and apply it not only to linear probing sort and bucket sort, where the bulk of the latency is due to random access, but also to the log–linear algorithm quicksort, where the access is primarily sequential, and again show agreement with experimental CPU times. With minor modifications, our model also fits CPU times previously reported by LaMarca and Ladner for radix sort, and by Rahman and Raman for most significant digit radix sort, Flashsort1, and memory tuned quicksort.