arXiv 1409.85242014-09cs.CCcs.DMcs.DS

最小可行倾斜问题

The Minimum Feasible Tileset problem

Yann Disser, Stefan Kratsch, Manuel Sorge

备注：: 23 pages, 2 figures. An extended abstract of this article appeared at the 12th Workshop on Approximation and Online Algorithms, Wroclaw, September 2014

摘要：

我们介绍和研究最小可行瓦片问题：给定一组符号和这些符号的子集（场景），找到最小可能数量的符号对（瓦片），使得每个场景可以通过从每个瓦片中选择最多一个符号来形成。我们表明，这个问题是APX硬，它是NP-硬，即使每个场景包含最多三个符号。我们的主要结果是一般情况下的4/3-近似算法。此外，我们表明，最小可行的Tilestion问题是固定参数听话的情况下，与符号的数量和数量的参数。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。