Output-sensitive algorithms for enumerating minimal transversals for some geometric hypergraphs

Abstract

We give a general framework for the problem of finding all minimal hitting sets of a family of objects in by another. We apply this framework to the following problems: (i) hitting hyper-rectangles by points in ; (ii) stabbing connected objects by axis-parallel hyperplanes in ; and (iii) hitting half-planes by points. For both the covering and hitting set versions, we obtain incremental polynomial-time algorithms, provided that the dimension d is fixed. © 2009 Springer Berlin Heidelberg.