流模型中覆盖和填充的近似方案
Approximation Schemes for Covering and Packing in the Streaming Model
摘要：
由Hochbaum和Maass提出的移位策略，以及Baker独立提出的移位策略，是一个统一的框架，用于设计NP-Hard问题的多项式逼近方案。这种策略已经在计算几何社区中的大量不同应用中取得了巨大的成功;最显着的是覆盖，包装和聚类问题。在本文中，我们重新审视的情况下，流模型的转移策略，并开发一个流友好的转移策略。当与Fonseca等人介绍的移动岩心集方法相结合时，我们获得了单位圆盘图的各种图形属性的流算法。作为进一步的应用，我们提出了新的近似算法和下界的单位盘覆盖（UDC）问题的流模型，目前没有算法是已知的。
英文摘要：
The shifting strategy, introduced by Hochbaum and Maass, and independently by Baker, is a unified framework for devising polynomial approximation schemes to NP-Hard problems. This strategy has been used to great success within the computational geometry community in a plethora of different applications; most notably covering, packing, and clustering problems. In this paper, we revisit the shifting strategy in the context of the streaming model and develop a streaming-friendly shifting strategy. When combined with the shifting coreset method introduced by Fonseca et al., we obtain streaming algorithms for various graph properties of unit disc graphs. As a further application, we present novel approximation algorithms and lower bounds for the unit disc cover (UDC) problem in the streaming model, for which currently no algorithms are known.
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