September 2008 - Vol. 51 No. 9

Interconnected Systems—the Internet, wireless networks, or sensor nets—embrace virtually all computing environments. Thus our data no longer needs to be stored, nicely organized, in centralized databases; it may instead span a great many heterogeneous locations and be connected through communication links. Records about stock-exchange transactions, for example, reside in broker firms and other financial entities […]

In this article, we study the problem of distributed selection from a theoretical point of view. Given a general connected graph of diameter D consisting of n nodes in which each node holds a numeric element, the goal of a k-selection algorithm is to determine the kth smallest of these elements. We prove that distributed selection indeed requires more work than other aggregation functions such as, e.g., the computation of the average or the maximum of all elements. On the other hand, we show that the kth smallest element can be computed efficiently by providing both a randomized and a deterministic k-selection algorithm, dispelling the misconception that solving distributed selection through in-network aggregation is infeasible.