Iterative Partial Rounding for Vertex Cover with Hard Capacities

We provide a simple and novel algorithmic design technique, for which we call itera-tive partial rounding, that gives a tight rounding-based approximation for vertex cover withhard capacities (VC-HC). In particular, we obtain an f -approximation for VC-HC on hy-pergraphs, improving over a previous results of Cheung et al (SODA 2014) to the tightextent. This also closes the gap of approximation since it was posted by Chuzhoy and Naorin (FOCS 2002). We believe that our rounding technique is of independence interests whenhard constraints are considered.Our main technical tool for establishing the approximation guarantee is a separationlemma that certifies the existence of a strong partition for solutions that are basic feasiblein an extended version of the natural LP.