Merging Multiple Lists in O(log n) Time

The problem of merging k (k \geqslant 2) sorted lists is considered. We give an optimal parallel algorithm which takes O\left( {\frac{{n\log k}} {p} + \log n} \right) time using p processors on the CREW PRAM, where n is the total size of the input lists. The algorithm can be seen as a unified algorithm for parallel sorting and merging. To obtain this algorithm, interesting techniques for designing algorithms are also discussed, including a new processor assignment strategy.