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引用次数: 0
摘要
本文针对直径有界的磁盘交集图的经典着色问题给出了一系列在线算法。我们的算法利用了此类图的几何表示法，并受到 Fiala 等人算法的启发，但具有更好的竞争比率。这种改进来自于在着色前使用了两种分割顶点集的技术。其中一种是平面 b 折叠着色的应用。这种方法更具通用性，我们展示了如何将其应用于平面上其他形状的着色，以及如何将其调整为在线 L(2,1)- 标记。
In this paper, we give a family of online algorithms for the classical coloring problem of intersection graphs of disks with bounded diameter. Our algorithms make use of a geometric representation of such graphs and are inspired by an algorithm of Fiala et al., but have better competitive ratios. The improvement comes from using two techniques of partitioning the set of vertices before coloring them. One of them is an application of a b-fold coloring of the plane. The method is more general and we show how it can be applied to coloring other shapes on the plane as well as adjust it for online -labeling.
期刊介绍：
Theoretical Computer Science is mathematical and abstract in spirit, but it derives its motivation from practical and everyday computation. Its aim is to understand the nature of computation and, as a consequence of this understanding, provide more efficient methodologies. All papers introducing or studying mathematical, logic and formal concepts and methods are welcome, provided that their motivation is clearly drawn from the field of computing.
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