Shifting Strategy for Geometric Graphs without Geometry

摘要

We give a simple framework as an alternative to the celebrated shifting strategy of Hochbaum and Maass [J. ACM, 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. We show how to obtain polynomial time approximation schemes (PTAS) for maximum (weighted) independent set problem on this graph class. Via a more sophisticated application of our framework, we also show how to obtain a PTAS for the maximum (weighted) independent set for intersection graphs of (low-dimensional) fat objects that are expressed without geometry.