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Plane geometric graph augmentation: a generic perspective
, 2011
"... Graph augmentation problems are motivated by network design, and have been studied extensively in optimization. We consider augmentation problems over plane geometric graphs, that is, graphs given with a crossingfree straightline embedding in the plane. The geometric constraints on the possible ne ..."
Abstract

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Graph augmentation problems are motivated by network design, and have been studied extensively in optimization. We consider augmentation problems over plane geometric graphs, that is, graphs given with a crossingfree straightline embedding in the plane. The geometric constraints on the possible new edges render some of the simplest augmentation problems intractable, and in many cases only extremal results are known. We survey recent results, highlight common trends, and gather numerous conjectures and open problems.