Logarithmic time cost optimal parallel sorting is not yet fast in practice!

When looking for new and faster parallel sorting algorithms for use in massively parallel systems it is tempting to investigate promising alterna tives from the large body of research done on parallel sorting in the eld of theoretical com puter science Such theoretical algorithms are mainly described for the PRAM Parallel RandomAccess Machine model of computation This paper shows how this kind of in vestigation can be done on a simple but versa tile environment for programming and measur ing of PRAM algorithms The practical value of Cole s Parallel Merge Sort algorithm have been investigated by comparing it with Batcher s bitonic sorting The O logn time consumption of Cole s algorithm implies that it must be faster than bitonic sorting which is O log n time if n is large enough How ever we have found that bitonic sorting is faster as long as n is less than i e more than Giga Tera items Consequently Cole s logarithmic time algorithm is not fast in prac tice Introduction and Motivation The work reported in this paper is an at tempt to lessen the gap between theory and practice within the eld of parallel computing Within theoretical computer science parallel al gorithms are mainly compared by using asymp totical analysis O notation This paper gives an example on how the analysis of implemented algorithms on nite problems provides new and more practically oriented results than those tra ditionally obtained by asymptotical analysis Parallel Complexity Theory A Rich