Enumerating minimal weight set covers

Zahi Ajami, Sara Cohen

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

4 Scopus citations


The weighted set cover problem is defined over a universe U of elements, and a set S of subsets of U, each of which is associated with a weight. The goal is then to find a subset C of S that collectively covers U, while having minimal weight. The decision version of this well-known problem is NP-complete, but approximation algorithms have been presented that are guaranteed to find a theta-approximation of the optimal solution, where theta is the harmonic sum of the size of the largest set in S. Finding minimal weight set covers is an important problem, used, e.g., in facility location, team formation and transaction summarization. This paper studies the enumeration version of this problem. Thus, we present an algorithm that enumerates all minimal weight set covers in polynomial delay (i.e., with polynomial time between results) in theta-approximate order. We also present a variant of this algorithm in order to enumerate non-redundant set covers in theta-approximate order. Experimental results show that our algorithms run well in practice over both real and synthetic data.

Original languageAmerican English
Title of host publicationProceedings - 2019 IEEE 35th International Conference on Data Engineering, ICDE 2019
PublisherIEEE Computer Society
Number of pages12
ISBN (Electronic)9781538674741
StatePublished - Apr 2019
Event35th IEEE International Conference on Data Engineering, ICDE 2019 - Macau, China
Duration: 8 Apr 201911 Apr 2019

Publication series

NameProceedings - International Conference on Data Engineering
ISSN (Print)1084-4627


Conference35th IEEE International Conference on Data Engineering, ICDE 2019

Bibliographical note

Publisher Copyright:
© 2019 IEEE.


  • Approximation algorithm
  • Enumeration
  • Set cover


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