The algorithm is essentially a pipeline algorithm; there are as many processors as there are values to sort. $$Each process in the pipeline maintains in its own memory the minimum value it has seen. $$When it receives a new value, it compares the new value to its min$-$so$-$far, and if the new value is larger, it is sent on to the next processor. $$If the new value is smaller, it becomes the new min$-$so$-$far, and the old min$-$so$-$far is sent on$.$The first value a processor receives becomes its first min$-$so$-$far, and is not sent on$.$The first process has access to the input array of unsorted values and initiates the pipeline. $$The last process will receive only one message, which will be the maximum in the array, and at that point the sort is complete, and the elements are in order in the pipeline. $$If the pipeline is ordered in MPI rank order, each processor has a partition of size one, and MPI$\_$Gather can be used to gather all the partitions into a single sorted array.