Approximation Schemes for Covering and Packing in the Streaming Model

The shifting strategy, introduced by Hochbaum and Maass [10], and independently by Baker [1], 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 [2, 5, 7, 8, 9]. 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. [6], 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. 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems