The Minimum Feasible Tileset Problem

Yann Disser, Stefan Kratsch, Manuel Sorge

Research output: Contribution to journalArticlepeer-review


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 APX-hard and that it is 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.

Original languageEnglish
Pages (from-to)1126-1151
Number of pages26
Issue number3
StatePublished - 15 Mar 2019


  • APX hardness
  • Approximation algorithm
  • Minimum feasible tileset
  • Parameterized complexity
  • Set packing

ASJC Scopus subject areas

  • General Computer Science
  • Computer Science Applications
  • Applied Mathematics


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