Dynamically computing the maxima of decomposable functions, with applications

The authors present a general technique for updating the maximum (minimum) value of a decomposable function as elements are inserted into and deleted from the set S. Applications of this technique include efficient algorithms for dynamically computing the diameter or closest pair of a set of points, minimum separation among a set of rectangles, smallest distance between a set of points and a set of hyperplanes, and largest or smallest area (perimeter) rectangles determined by a set of points. The main appeal of the approach lies in its generality. Several research directions suggested by the work are noted