Normalized divide-and-conquer: A scaling technique for solving multi-dimensional problems

A new technique, named normalized divide-and-conquer,is presented to solve multi-dimensional problems on a grid in a very efficient way. It is also shown that a number of problems concerning objects in arbitrary space can be transformed into problems on a grid by using another form of normalization. In this way, new solutions are obtained for the multi-dimensional maximal elements and rectangle intersection problem that are more efficient than previous solutions.