The Minimum Feasible Tileset Problem

• Published in: Algorithmica Vol. 81; no. 3; pp. 1126 - 1151
• Main Authors: Disser, Yann, Kratsch, Stefan, Sorge, Manuel
• Format: Journal Article
• Language: English
• Published: New York Springer US 15.03.2019; Springer Nature B.V
• Subjects: Algorithm Analysis and Problem Complexity; Algorithms; Computer Science; Computer Systems Organization and Communication Networks; Data Structures and Information Theory; Feasibility studies; Mathematics of Computing; Symbols; Theory of Computation; APX hardness; Minimum feasible tileset; Approximation algorithm; Parameterized complexity; Set packing
• ISSN: 0178-4617; 1432-0541
• DOI: 10.1007/s00453-018-0460-3

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.