A unified approach to approximating partial covering problems

Jochen Könemann, Ojas Parekh, Danny Segev

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish
Title of host publicationAlgorithms, ESA 2006 - 14th Annual European Symposium, Proceedings
PublisherSpringer Verlag
Number of pages12
ISBN (Print)3540388753, 9783540388753
StatePublished - 2006
Externally publishedYes
Event14th Annual European Symposium on Algorithms, ESA 2006 - Zurich, Switzerland
Duration: 11 Sep 200613 Sep 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4168 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference14th Annual European Symposium on Algorithms, ESA 2006

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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