论文标题
稀疏班级的统治和独立问题的一般内核化技术
A general kernelization technique for domination and independence problems in sparse classes
论文作者
论文摘要
我们通过定义水百合来统一和扩展稀疏类[6,17]中的先前核酸化技术，并显示如何在有限的扩展类中使用它们，以构建（R，C）域名集合（R，C）划分的线性自行车，（R，C） - 散布集，R-dounaMination，R-DAIMANIAN，ROMAN，R-ROMAN，ROMAMAN，ROMAMAN，ROMAMAN，ROMAMAN，ROMAMAN，ROMAMAN，ROMANTIAN，我们调用的问题（RIK，RIK，RIK，RIK，r，r，rik nip [λ，λ） R完美代码）。以稍微更改输出图类的成本，我们的自行车可以变成内核。 我们进一步证明了如何将这些构造组合起来创建“多级别”，这意味着图表代表多个问题的内核。具体而言，我们证明了R-Ropination集合，R-Roman Dodination的总R-ROMAN DONATION承认了多级别。以及R-DR-OPIOMINATION SET和2R无关的集合，以一次为R的多个值。
We unify and extend previous kernelization techniques in sparse classes [6,17] by defining water lilies and show how they can be used in bounded expansion classes to construct linear bikernels for (r, c)-Dominating Set, (r, c)-Scattered Set, Total r-Domination, r-Roman Domination, and a problem we call (r, [λ, μ])-Domination (implying a bikernel for r-Perfect Code). At the cost of slightly changing the output graph class our bikernels can be turned into kernels. We further demonstrate how these constructions can be combined to create 'multikernels', meaning graphs that represent kernels for multiple problems at once. Concretely, we show that r-Dominating Set, Total r-Domination, and r-Roman Domination admit a multikernel; as well as r-Dominating Set and 2r-Independent Set for multiple values of r at once.
