The following two computational problems are studied: Duplicate grouping: Assume that n items are given, each of which is labeled by an integer key from the set 0,..., U � 1 4. Store the items in an array of size n such that items with the same key occupy a contiguous segment of the array. Closest pair: Assume that a multiset of n points in the d-dimensional Euclidean space is given, where d � 1 is a fixed integer. Each point is represented as a d-tuple of integers in the range 0,..., U � 14 Ž or of arbitrary real numbers.. Find a closest pair, i.e., a pair of points whose distance is minimal over all such pairs.