Nonoverlapping local alignments (weighted independent sets of axis-parallel rectangles) Original Research Article

We consider the following problem motivated by an application in computational molecular biology. We are given a set of weighted axis-parallel rectangles such that for any pair of rectangles and either axis, the projection of one rectangle does not enclose that of the other. Define a pair to be independent if their projections in both axes are disjoint. The problem is to find a maximum-weight independent subset of rectangles.