Average case analysis of a greedy algorithm for the minimum hitting set problem

Abstract

Let k be fixed. Let n and m denote integers and C = {C ₁,...,C _m} a family of m subsets drawn from an n-element set C. A subset H $\subseteq$ C is a hitting set for the family C if H has a non-empty intersection with each element of this family and the minimum hitting set problem is that of finding a hitting set of minimum cardinality. The purpose of this paper is to study the efficiency of a natural greedy algorithm for the approximate solution of the minimum hitting set probl em when C is a random family of k-element subsets, k fixed, and when n and m tend to ∞ with $\tfrac{m}{n}$ = α, a fixed constant.