The Minimum Feasible Tileset problem
Abstract
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.
Cite
@article{arxiv.1409.8524,
title = {The Minimum Feasible Tileset problem},
author = {Yann Disser and Stefan Kratsch and Manuel Sorge},
journal= {arXiv preprint arXiv:1409.8524},
year = {2017}
}
Comments
23 pages, 2 figures. An extended abstract of this article appeared at the 12th Workshop on Approximation and Online Algorithms, Wroclaw, September 2014