TY - GEN

T1 - A unified approach to approximating partial covering problems

AU - Könemann, Jochen

AU - Parekh, Ojas

AU - Segev, Danny

PY - 2006

Y1 - 2006

N2 - 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 prizecollecting 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 π(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 present a unified framework for approximating problems that can be formulated or interpreted as special cases of generalized partial cover. We demonstrate the applicability of our method on a diverse collection of covering problems, for some of which we obtain the first non-trivial approximability results.

AB - 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 prizecollecting 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 π(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 present a unified framework for approximating problems that can be formulated or interpreted as special cases of generalized partial cover. We demonstrate the applicability of our method on a diverse collection of covering problems, for some of which we obtain the first non-trivial approximability results.

UR - http://www.scopus.com/inward/record.url?scp=33750684328&partnerID=8YFLogxK

U2 - 10.1007/11841036_43

DO - 10.1007/11841036_43

M3 - Conference contribution

AN - SCOPUS:33750684328

SN - 3540388753

SN - 9783540388753

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 468

EP - 479

BT - Algorithms, ESA 2006 - 14th Annual European Symposium, Proceedings

PB - Springer Verlag

T2 - 14th Annual European Symposium on Algorithms, ESA 2006

Y2 - 11 September 2006 through 13 September 2006

ER -