, Volume 81, Issue 3, pp 1126–1151 | Cite as

The Minimum Feasible Tileset Problem

  • Yann Disser
  • Stefan Kratsch
  • Manuel SorgeEmail author


We introduce and study the Minimum Feasible Tileset problem: given a set of symbols and subsets of these symbols (scenarios), find a smallest possible number of pairs of symbols (tiles) such that each scenario can be formed by selecting at most one symbol from each tile. We show that this problem is \(\mathsf {APX}\)-hard and that it is \(\mathsf {NP}\)-hard even if each scenario contains at most three symbols. Our main result is a 4/3-approximation algorithm for the general case. In addition, we show that the Minimum Feasible Tileset problem is fixed-parameter tractable both when parameterized with the number of scenarios and with the number of symbols.


Set packing Approximation algorithm APX hardness Parameterized complexity Minimum feasible tileset 


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Authors and Affiliations

  1. 1.Institut für Mathematik, Graduate School CETU DarmstadtDarmstadtGermany
  2. 2.Institut für InformatikHumboldt-Universität zu BerlinBerlinGermany
  3. 3.Institut für Softwaretechnik und Theoretische InformatikTU BerlinBerlinGermany
  4. 4.Department of Industrial Engineering and ManagementBen Gurion University of the NegevBeer ShevaIsrael

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