A time- and communication-optimal distributed sorting algorithm in a line network and its extension to the dynamic sorting problem

This paper presents a strictly time- and communication-optimal distributed sorting algorithm in a line network. A strictly time-optimal distributed sorting algorithm in a line network has already been designed. However, its communication complexity is not strictly optimal and it seems to be difficult to extend it to other problems, such as that related to multiple elements in a process, and also the dynamic sorting problem where the number of elements each process should have as its solution is not the same as that in the initial state. Therefore, the algorithm in this paper was designed by an alternative approach to make it strictly time- and communication-optimal. Moreover, an extension to the dynamic sorting problem is described.