The Budgeted Unique Coverage Problem and Color-Coding

  • Authors:

  • Neeldhara Misra;Venkatesh Raman;Saket Saurabh;Somnath Sikdar

  • Affiliations:

  • The Institute of Mathematical Sciences, Chennai, India;The Institute of Mathematical Sciences, Chennai, India;University of Bergen, Bergen, Norway;The Institute of Mathematical Sciences, Chennai, India

  • Venue:
  • CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

Abstract

We show, by a non-trivial application of the color-coding method of Alon et al.[2], that Budgeted Unique Coverage (a variant of Set Cover ) is fixed-parameter tractable, answering an open problem posed in [13]. We also give improved fixed-parameter tractable algorithms for two special cases of Budgeted Unique Coverage : Unique Coverage (the unweighted version) and Budgeted Max Cut . To derandomize our algorithms we use an interesting variation of k -perfect hash families known as (k ,s )-hash families which were studied by Alon et al.[1] in the context of a class of codes called parent identifying codes [3]. In this setting, for every s -element subset S of the universe, and every k -element subset X of S , there exists a function that maps X injectively and maps the remaining elements of S into a different range. We give several bounds on the size of (k ,s )-hash families. We believe that our application of color-coding may be used for other problems and that this is the first application of (k ,s )-hash families to a problem outside the domain of coding theory.