Parameterized complexity of red blue set cover for lines

Pradeesha Ashok, Sudeshna Kolay, Saket Saurabh

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


We investigate the parameterized complexity of Generalized Red Blue Set Cover (Gen-RBSC), a generalization of the classic SetCover problem and themore recently studied Red Blue Set Cover problem. Given a universe U containing b blue elements and r red elements, positive integers kℓ and kr, and a family F of ℓ sets over U, the Gen-RBSC problem is to decide whether there is a subfamily Fℓ⊆ F of size at most kℓ that covers all blue elements, but at most kr of the red elements. This generalizes Set Cover and thus in full generality it is intractable in the parameterized setting, when parameterized by kℓ + kr. In this paper, we study Gen-RBSC-lines, where the elements are points in the plane and sets are defined by lines.We study this problem for the parameters kℓ, kr, and kℓ + kr. For all these cases, we either prove that the problem is Whard or show that the problem is fixed parameter tractable (FPT). Finally, for the parameter kℓ + kr, for which Gen-RBSC-lines admits FPT algorithms, we show that the problem does not have a polynomial kernel unless co-NP ⊆ NP/poly. Further,we showthat theFPTalgorithm does not generalize to higher dimensions.

Original languageEnglish
Title of host publicationLATIN 2016
Subtitle of host publicationTheoretical Informatics - 12th Latin American Symposium, Proceedings
EditorsGonzalo Navarro, Evangelos Kranakis, Edgar Chávez
PublisherSpringer Verlag
Number of pages14
ISBN (Print)9783662495285
StatePublished - 1 Jan 2016
Externally publishedYes
Event12th Latin American Symposium on Theoretical Informatics, LATIN 2016 - Ensenada, Mexico
Duration: 11 Apr 201615 Apr 2016

Publication series

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


Conference12th Latin American Symposium on Theoretical Informatics, LATIN 2016

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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