Output-Sensitive Algorithms for Enumerating Minimal Transversals for Some Geometric Hypergraphs

We give a general framework for the problem of finding all minimal hitting sets of a family of objects in Rd by another. We apply this framework to the following problems: (i) hitting hyper-rectangles by points in Rd ; (ii) stabbing connected objects by axis-parallel hyperplanes in Rd ; 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.

• Type: Conference
• Year: 2009
• Where: ESA
• Authors: Khaled M. Elbassioni, Kazuhisa Makino, Imran Rauf
• Keywords: Algorithms, ESA 2009, Hitting Set, Hitting Set Versions, Minimal Hitting Sets