Network partition and its application to distributed selection problem

The authors discuss the network partition and the distributed selection problems for a general tree network. The distributed selection problem is to select the k-th smallest element of a set N of elements distributed among nodes of a point-to-point asynchronous communication network. The distributed algorithms considered are primarily message driven. All the messages have a fixed length, and may carry only a limited amount of information. The authors assume the network is sufficiently reliable so that the messages sent in a link are received error free by the receiver node in first-in-first-out (FIFO) order with finite but totally unpredictable delays. The authors present an improved selection algorithm for general tree networks. Based on the conventional reduction strategy, they introduce a tree partition technique to localize the message passing and therefore to reduce the total message complexity