We give a simple framework which is an alternative to the celebrated and widely used shifting strategy of Hochbaum and Maass (J. ACM 32(1):103–136, 1985) which has yielded efficient algorithms with good approximation bounds for numerous optimization problems in low-dimensional Euclidean space. Our framework does not require the input graph/metric to have a geometric realization—it only requires that the input graph satisfy some weak property referred to as growth boundedness. Growth bounded graphs form an important graph class that has been used to model wireless networks. We show how to apply the framework to obtain a polynomial time approximation scheme (PTAS) for the maximum (weighted) independent set problem on this important graph class; the problem is W[1]-complete.
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