Algorithms for Implicit Hitting Set Problems

A hitting set for a collection of sets is a set that has a nonempty intersection with each set in the collection; the hitting set problem is to find a hitting set of minimum cardinality. Motivated by instances of the hitting set problem where the number of sets to be hit is large, we introduce the notion of implicit hitting set problems. In an implicit hitting set problem the collection of sets to be hit is typically too large to list explicitly; instead, an oracle is provided which, given a set H, either determines that H is a hitting set or returns a set that H does not hit. We show a number of examples of classic implicit hitting set problems, and give a generic algorithm for solving such problems optimally. The main contribution of this paper is to show that this framework is valuable in developing approximation algorithms. We illustrate this methodology by presenting a simple on-line algorithm for the minimum feedback vertex set problem on random graphs. In particular our algori...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Karthekeyan Chandrasekaran, Richard Karp, Erick Moreno-Centeno, Santosh Vempala
• Keywords: CORR 2011, Education, Feedback Vertex, Hitting Set, Minimum Cardinality