通过核化的传播：顶点覆盖约束
Propagation via Kernelization: The Vertex Cover Constraint
摘要：
核化的技术在于从问题的实例中提取一个本质上等价的实例，该实例的大小以参数k为界。除了作为有效的参数化算法的基础之外，该方法还提供了在约束规划的上下文中进行推理的丰富信息。我们研究使用核化设计传播通过顶点覆盖约束的例子。由于经典的核化规则往往对应于优势，而不是一致性，我们引入了“无损”内核的概念。虽然我们的初步实验结果显示了这种方法的潜力，但也显示了它的一些局限性。特别是，这种方法对于大型和稀疏图的顶点覆盖更有效，因为它们往往具有相对较小的内核。
英文摘要：
The technique of kernelization consists in extracting, from an instance of a problem, an essentially equivalent instance whose size is bounded in a parameter k. Besides being the basis for efficient param-eterized algorithms, this method also provides a wealth of information to reason about in the context of constraint programming. We study the use of kernelization for designing propagators through the example of the Vertex Cover constraint. Since the classic kernelization rules often correspond to dominance rather than consistency, we introduce the notion of "loss-less" kernel. While our preliminary experimental results show the potential of the approach, they also show some of its limits. In particular, this method is more effective for vertex covers of large and sparse graphs, as they tend to have, relatively, smaller kernels.
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