Shifting Strategy for Geometric Graphs without Geometry

We give a simple framework which is an alternative to the celebrated and widely used 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. 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 schemes (PTAS) for maximum (weighted) independent set problem on this important graph class; the problem is W[1]-complete. Via a more sophisticated application of our framework, we 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. Erlebach...

• Type: Conference
• Year: 2009
• Where: ISAAC
• Authors: Imran A. Pirwani
• Keywords: Algorithms, Important Graph Class, Independent Set Problem, Intersection Graphs, ISAAC 2009