Well if you'd like to select the k-th biggest element from a distributed array it's impractical - if not impossible - to send everything to one machine so another approach is needed. A fairly simple algorithm would select a pivot randomly on a random node and broadcast it to all other nodes. Each node then does the partitioning locally and counts partition sizes. Now you do a sum all-reduction on the sizes to decide which side you need to recurse on. This takes logarithmically many rounds in expectation just like the sequential algorithm, but it could result in very unbalanced work if the data isn't distributed randomly. It also has even more trouble if the pivot selection is bad because of the communication overhead. There are various techniques to overcome these challenges but it's a bit much to go into here.