A Unified Approach to Approximating Partial Covering Problems

  • Jochen Könemann
  • Ojas Parekh
  • Danny Segev
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4168)


An instance of the generalized partial cover problem consists of a ground set U and a family of subsets \({\cal S} \subseteq 2^U\). Each element eU is associated with a profit p(e), whereas each subset \(S \in {\cal S}\) has a cost c(S). The objective is to find a minimum cost subcollection \({\cal S}' \subseteq {\cal S}\) such that the combined profit of the elements covered by \({\cal S}'\) 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 eU uncovered, we incur a penalty of π(e). The goal is to identify a subcollection \({\cal S}' \subseteq {\cal S}\) that minimizes the cost of \({\cal S}'\) 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.


Vertex Cover Partial Cover Approximation Guarantee Discrete Apply Mathematic Partial Vertex Cover 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jochen Könemann
    • 1
  • Ojas Parekh
    • 2
  • Danny Segev
    • 3
  1. 1.Department of Combinatorics and OptimizationUniversity of WaterlooCanada
  2. 2.Department of Mathematics and Computer ScienceEmory UniversityUSA
  3. 3.School of Mathematical SciencesTel-Aviv UniversityIsrael

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