A Unified Approach to Approximating Partial Covering Problems

An instance of the generalized partial cover problem consists of a ground set U and a family of subsets S 2U . Each element e U is associated with a profit p(e), whereas each subset S S has a cost c(S). The objective is to find a minimum cost subcollection S S such that the combined profit of the elements covered by S is at least P, a specified profit bound. In the prize-collecting version of this problem, there is no strict requirement to cover any element; however, if the subsets we pick leave an element e U uncovered, we incur a penalty of (e). The goal is to identify a subcollection S S that minimizes the cost of S plus the penalties of uncovered elements. Although problem-specific connections between the partial cover and the prize-collecting variants of a given covering problem have been explored and exploited, a more general connection remained open. The main contribution of this paper is to establish a formal relationship between these two variants. As a result, we prese...

• Type: Conference
• Year: 2006
• Where: ESA
• Authors: Jochen Könemann, Ojas Parekh, Danny Segev
• Keywords: Algorithms, ESA 2006, Generalized Partial Cover, Partial Cover Problem, Specified Profit Bound