Discovering Large Empty Maximal Hyper-Rectangle in Multi-Dimensional Space

Given a collection of points in a multi-dimensional space, we consider the problem of nding the set of all possible Maximal Hyper-Rectangle (MHR), deened to be hyper-rectangles that are empty and have at least a point bounding each of its surfaces. It is easy to see that there are enormous number of such MHRs in a given instance, and most of the time, applications require only to nd the \largest" MHR or\suuciently large" MHRs. Our proposed algorithm solved all the above problems by setting a criterion to measure suuciently large MHRs so that only those large MHRs will be reported. The algorithm runs much faster when the criterion set is \reasonably tight" as pruning is done naturally in the algorithm.