An abundance of real-world problems manifest as covering edges and/or vertices of a graph with cliques that are optimized for some objectives. We consider different structural parameters of graph, and design fixed-parameter tractable algorithms for a number of clique cover problems. Using a set representation of graph, we introduce a framework for computing clique cover with different objectives. We demonstrate use of the framework for a variety of clique cover problems. Our results include a number of new algorithms with exponential to double exponential improvements in the running time.
翻译:大量真实世界的问题表现在覆盖边缘和/或圆顶上, 以图表为圆柱形的图形为覆盖边缘和/ 或顶点, 以达到某些目标。 我们考虑不同的图形结构参数, 并为一些分类覆盖问题设计固定参数可移动的算法 。 我们用一组图表来引入一个框架, 用于计算具有不同目标的分类覆盖。 我们展示了对各种分类覆盖问题的框架的使用 。 我们的结果包括一系列新的算法, 以指数化方式在运行时间上实现双倍指数式改进 。