  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.
